It must be remembered that strictly speaking before the Enlightenment Protestantism on a social level was quite Liberal and Progressive. It was rejecting the conservative norms. It wasn't looking back, it was looking ahead. Only after the Enlightenment shift was underway and decimating the church and society did Protestants start to look back with longing.
This Progressivism sought to re-form Christendom. Sometimes this was in terms of a Protestant bloc, but often it was in terms of the growing Nationalism that was developing in the new state-empowered era. In this era and way of thinking (which is still with us) proto-Protestants were viewed through a Nationalistic or Tribal lens. In many ways this both a pre-cursor and overlaps with what the Romantic Movement would be doing with the Middle Ages. They would re-cast history and form narratives in order to meet the propaganda needs and desires of the present. The times of yore were magnified and glorified in order to demand social change.
Celtic Christians, Lollards and Hussites would become fodder for Nationalist sympathies and their project to sacralize the state and society, forging a social consensus. While successful in individual nation states those who employed these narrative in order to form a Protestant International, a united Protestant Christendom, ultimately failed.
Other Protestants don't think in these terms at all. Many are virtually unaware of the massive role the Magistrates played in the 16th century Reformation. They view it strictly in religious terms and are hostile to any attempts to explain the Reformation in terms of sociology. Many Revisionist historians err in discounting religious motive, but many Christians err in failing to grasp context.
And today as Cathedrals and Crusades are once more venerated, they are unsure how to view the people of the Middle Ages who rejected Rome.
In fact many Protestant Church Histories almost ignore the proto-Protestants. They always mention Wycliffe and Hus but they never really tell the story of the Lollards and Hussites. The Waldensians are almost ignored. If they do mention much it's usually in connection with the post-Reformational Waldensians in the Cottian Alps who were assaulted in the 17th century. They quote Milton's poem, maybe mention Cromwell's threats and the story ends.
19th century historians like Wylie and D'Aubigne spend more time on them. They did not wish to emphasize continuity with the medieval Church. And yet, they quite irresponsibly ignore and in the case of Wylie grossly and deliberately understate what happened with the Hussites after Huss. Not all the chapters in Hussite history are glorious and it's a poor historian indeed who chooses to omit what might harm the narrative he seeks to weave.
These historians and certainly Protestant historians of our day will certainly neglect and avoid the painful but patent reality that the Reformation did undo the social consensus in Western Europe. The Roman Catholic Church was the foundation of Medieval Christendom. If you wanted to answer any social or legal question, Rome provided the framework for the answer. With this foundation smashed, men had to look elsewhere. 'The Bible' was the answer many gave and yet no one could agree on what it taught. Men struggled to find ways to lay new foundation stones for the social order. Some looked to laws of nature, others formulated ideas regarding the Divine Right of kings.
While it certainly was not the intention or goal of the Reformation, it can hardly be denied that in many ways it laid the path that led to the Enlightenment. By undoing the social consensus and seeking to create a new one, the Magisterial Reformation opened the door to Secularism and the growth of the state as the foundation of society.
The Enlightenment can even be viewed as a continuation of the Reformation. Liberal Christians think in these terms. The Enlightenment was for them in many ways the telos, the end goal of the Reformation.
You can't of course blame Luther and Calvin for the Enlightenment but unwittingly they opened doors which allowed their bane to enter. Or to put it another way, they created a new branch of Christendom, but in order to do so they started a boulder rolling down a mountain. They didn't want it to roll too far but by the time they tried to get it to stop, it was too late and like it not their descendants would have to go along for the ride.
This whole perspective is totally missed by most Protestants but is key to understanding how Roman Catholics and Eastern Orthodox view the flow of Church History. For the Orthodox, Protestantism is inseparable from Roman Catholicism and is simply the child of late medieval Scholasticism.
Many factions will reach into the past, often in an anachronistic fashion and try to claim various groups as continuous with their own. There are Presbyterians who try and claim the Waldensians were all but Presbyterians. I've seen Presbyterians and recently even Theonomists attempt to claim Celtic Christianity as somehow emulating their viewpoint. It's an outrageous travesty.
Of course many Baptists are quite keen to find historical precedent and vindication in identifying with these various groups. Others would accuse me of doing the same. While I am certainly doing this in one sense, I'm arguing it's far more complicated and I would certainly argue that virtually none of these groups are represented today. The vision of the medieval Dissenter has been all but lost. Ironically it wasn't the Inquisition that destroyed it. That devilish monstrosity certainly did its part. But ultimately it was the temptation of power that came with the Reformation...the same temptation that the early Church succumbed to in the Constantinian Shift.
There is some truth to some of these claims of continuity. Certainly groups like the Lollards were arguing for the principles of Sola Scriptura even if they weren't employing that exact terminology. Hence they were quite hostile to many aspects of the Roman Catholic system. Wycliffe himself never abandoned the idea of the sacral state-church unity. With regard to the Lollards the testimony is mixed. Were they followers of Wycliffe or did they (as some strongly argue) antedate him? They didn't teach Sola Fide (Justification by Faith Alone), but they did argue the Bible was the standard for all Christian doctrine, itself a rejection of Romanism.
So what became of the Lollards? They disappeared with the Reformation because they joined it. In fact in 'Albion's Seed' DH Fischer argues East Anglia was the center of Lollard activity, their area of highest concentration. This same area, Norfolk, Suffolk, and Essex would later become the cradle of Puritanism.
So was Puritanism (in some sense) the heir of Lollardy? Yes, in some sense. And yet they are of course not exactly the same, and neither group was entirely monolithic. In fact perhaps it could be argued someone like Richard Baxter might have taught a system more compatible or akin to the Lollard way of thinking. Baxter was respected by many, but many Puritans considered him to be a heretic who denied Justification by Faith Alone.
The Hussites were also divided. The Utraquists were still mostly Roman Catholic in mentality and the Taborites were definitely more extreme, more determined to follow through with Biblical reform. The Taborites and their violent nationalist agenda did not survive. Instead, Utraquism continued and later would blend nicely with Lutheranism and the more Biblically conservative groups would reject Tabor's violence. Influenced by men like Petr Chelcicky (who was highly critical of Tabor) they would go on to form the Unitas Fratrum or the Bohemian Brethren as they are sometimes known. Interestingly this group did not 'join' with the main Reformation bodies but continued on its own separate path. Under the leadership of Lucas of Prague many of Chelcicky's ideas were destroyed and he moved them to a more centrist and compromised position. Later after the Thirty Years War they would seek refuge in Germany and through contacts with German Pietism be transformed into the Moravians.
So can the Lutherans or Reformed 'claim' the Hussites as somehow being precursors to their own belief systems? In some ways. Yes, some of the Hussite groups were committed to Scriptural fidelity, but these are not the ones who later joined with the Magisterial Protestantism. Those that did (the Utraquists) were less committed to the principle of Sola Scriptura. The Taborites and Utraquists certainly thought in terms of state Christianity. They just wanted it their way. Only the followers of Chelcicky, the Chelcice Brethren and the later Unitas would reject the entire Constantinian construct.
The Waldensians are others 'claimed' by Magisterial Protestantism but this is most doubtful. The Waldensians have often been identified as two main bodies, the Poor of Lyons and the Poor Lombards. The Lyons group was basically restricted to France and was a little less Biblicist. The Lombard group spread across Italy, Austria, Germany, Hungary (which today includes swathes of Croatia, Romania and Slovakia) and certainly Bohemia and Moravia, today's Czech Republic.
This group wasn't monolithic either and had no central institutionalized structure. For many this alone is a problem. For many ecclesiastical thinkers institutionalization is 'the' mark of the Church and its claims to legitimacy. The Waldensians functioned as congregations in many cases visited by wandering teachers.
Apart from their strict Biblicism their other hallmark position was a rejection of Constantinianism. They rejected the idea of the Church being wedded to worldly power. Power (and its twin Wealth) represents violence and coercion, a kingdom antithetical to the Spiritual Kingdom established by the Holy Spirit. These groups dated this shift to the Donation of Constantine when Constantine supposedly gave the Pope political reign over Western Europe. Up until the Renaissance people believed this document was legitimate and dated to the 4th century. At that time it was discovered to be a forgery, probably composed during the time of Charlemagne.
Nevertheless even if the foundational documents were a fraud, the principles they represented were the reality. The Waldensians rejected this on theological grounds. It doesn't matter if the Donation was a forgery, it was just a tool the Papacy used to support their argument for the principle.
Unlike the medieval Catholic Church and our contemporary American Church, the Waldensians rightly understood that money and wealth were the foundations of power. Their denunciation of riches and embracing poverty was no mere rejection of worldly goods and materialism. This wasn't some kind of monkish asceticism. This was a principled rejection of the world system, the impulse to seek one's own advantage...to the disadvantage of others. It was a refusal to compromise with a world system and to accept the ethics that it demands.
Money buys and affords influence, security, and respectability...things incompatible with the Christian Ethic laid out by Christ Himself.
Riches lead to ownership, manipulation and the exploitation of others which are all forms of violence. Money is power, poverty is a rejection of not just money, but power. That's the key to understanding their devotion to poverty.
And poverty doesn't have to mean living in rags. The Waldensians lived but in refusing to compromise they were often on the fringes of society. Even this wasn't static. There are stories of Waldensians become weavers because it afforded them a cover for travel and meetings. Some did well enough financially and there are times when groups of Waldensians would have to examine themselves and purge the worldliness they had embraced. But generally speaking their fidelity led them to impoverishment and often they lived semi-communally out of ideology and for both security and the ability to maximize resources.
The Roman Catholic Church was forced to answer this because this call for poverty absolutely resonated with the public and thousands joined the various Waldensian groups. The 11th and 12th centuries saw the Papacy grow not only in terms of political power but in wealth and extravagance.
The Papacy sought to employ the Franciscans as a sort of Roman Catholic answer to Waldensianism. This didn't go so well at first as many Franciscans ended up turning on Rome. But eventually the Franciscans coupled with the activities of groups like the Dominicans did much to arrest the growth of Biblical Christianity.
These groups also worked to counter the Cathars who also preached a message of poverty but in their case was mixed with a Gnostic cosmology and spirituality.
The Magisterial Reformation categorically rejected this view and the Waldensians who joined with Protestantism abandoned this viewpoint. They succumbed to the temptation of security and respectability, even power that the New Constantinianism, the Reformation offered to them.
The only groups that rejected this were the Anabaptists. Some see continuity between the Waldensians and the Anabaptists and it is very probable. This is an old debate regarding Anabaptist origins. Did they arise out of the Reformation and break off very early or were they in fact the result of proto-Protestant ideology at work? There's probably some truth to both positions.
Does that mean the Waldensians rejected infant baptism? The overwhelming testimony is in the negative. They accepted it and certainly Chelcicky (who some believe may have been a Waldensian affiliate) didn't reject it.
Were some of them ideologically Donatist? Did they re-baptise, re-do Roman Catholic baptism? Yes, but that doesn't mean they (or the Donatists) were Baptist. The Baptist argument is that only believers who can articulate their faith, thus requiring a certain age, can be baptised. This was not the view of the Donatists or certainly the majority of theWaldensians. Far from being Baptists the Donatists most certainly baptised and communed infants and I would argue the Waldensians did the same.
There were some small groups floating around during this period who were Baptistic but that was not the hallmark of pre-Reformational protest. It doesn't defeat the Baptist argument per se, but an appeal to proto-Protestantism doesn't make their case.
For others the difficulty arises with the whole question of institution. They grow uncomfortable appealing to proto-Protestant groups because they lacked coherence and the key article of the Reformation, the Lutheran formula of Justification. Luther said this was the article by which the Church stood or fell. Of course Rome had never embraced this doctrine, but in the tortured logic of the institutionalist the fact that they hadn't formally denied it (itself an absurd possibility since it didn't exist prior to Luther)... Rome was still the True Church.
Thus Protestantism has never really wished to claim the Church of the Middle Ages was underground and hiding in caves and forests. This way they can claim the heritage of the medieval West and declare continuity. The Culture War minded Church of our present day is even more determined to ally with Roman Catholicism in the fight against secularism and less interested in the message the Waldensians and others who rejected power.
Where was your Church prior to Luther? This is the deafening charge ringing in the ears of many Protestants and every faction whether Reformed, Lutheran or Anglican has sought to answer it in their own way. But Rome is begging the question assuming the Church exists in institutional forms that can be pointed to. All institutionalists have sought bureaucratic forms to instigate and maintain 'unity' and have never been able to find it. Biblicists have always argued the unity is Spirit-wrought and doesn't require adding additional ecclesiastical forms or structures to the Biblical model of independent congregations existing in fellowship with one another. Unity resting in institutional forms at best creates an empty shell, a veneer.