OTL, the Matter of Arthur as we know it today was largely envisioned by medieval troubadours in the French tradition, and the nobles who patronized the Arthurian cycle were Norman French. They may have liked the timing of the legends to be pre-Anglo-Saxon, which made the English people they had subjugated the bad guys and the French invaders--some of whom had ties to Brittany, where some native Britons had fled the wave of germanic invaders who became the "English," as the vicarious heirs of the Arthurian days.
So--insofar as the chivalric troubadour traditions were an alternative to strict and proper Christianity as preached by the Church in their times, the romances were something of a heresy in their day OTL.
To take it farther, the tradition would have to put down deeper grassroots in the common folk, whereas the Matter of Arthur was popular among protective ruling classes in England precisely because it set the nobility apart from, and above, the common English masses. Over time to be sure the common English came to accept Arthurian romance as part of their own heritage and not an opposition to it, but I suspect by the time that fusion was properly accomplished (we can see it in Chaucer's time, particularly in the more Northern and less Frenchified Sir Gawain and the Green Knight) England and Europe in general were nearing the end of the Medieval period and verging on an era where religious upheaval would take a more Protestant sort of form.
Conceivably one might have some sort of anti-Protestantism, insofar as one categorizes Protestantism as a tendency to "purify" Christianity to a more austere, pruned Gospel/Augustinian viewpoint of strict monotheism suspicious of the quasi-pagan elaborations of classic Catholicism, so that Anglicanism is on one end of the spectrum and such Calvinists as ruled in Scotland are on another end. Supposing some proto-Protestant "heresy" removed Britain from the Catholic ambit as early as say 1400 or so, somehow, and in reaction the common people, not as prepared for such separation as they would be in Elizabeth's day OTL, along with dissident factions of nobles, were forced to develop a counterculture underground mimicking and maintaining the syncretism and pageantry of Roman Catholicism but prevented from simply declaring themselves Catholics in rebellion. Possibly, if the British authorities of the "Protestant" cult were strong enough to deny dissenters contact and communication with the Roman church and yet not able to bring them around to supporting the state cult, a counter cult based on a hodgepodge of Arthurian romance and folk memory of Catholic practice and doctrine might emerge, and given enough time--say to 1650 or so--to fester as a repressed folk religion, whereupon the repressive central regime collapses somewhere in England and the populist Arthurians manage to come to power at last and find to their shock and horror their evolved faith is incompatible with the Roman church they had always believed themselves faithful to, the alternate creed might at long last have a seat and a shot at becoming the state religion in Britain, if the Arthurians manage to overwhelm the heirs of the Proto-Protestants.
Or maybe it is more plausible that at some point the proto-Protestant regime moves on to new generations that don't feel as driven to impose their theology on the resistant masses, and do think that if the British people are not Catholics that would be good enough, and tolerate open Arthurianism (as the post-Glorious-Revolution Orangeist/Hanoverian UK resolved to tolerate Catholicism OTL--at arms length, with great suspicion and within tight limits) hoping it will displace actual Catholicism from returning, which it does, and then over time the Arthurians gain the upper hand in the realm.
I can see them instituting a new grass roots dynasty raised out of some dissenting country noble line, naming their sons with royal ambitions names like Arthur, Gawain, Galahad--not so sure if any prince would ever be named "Lancelot" though, it would be a little bit like naming a kid "Judas!" Similarly would any girl ever be named "Guinevere?" But aren't a number of common names of OTL in English variants on Arthurian names? (Is "Jennifer" in fact a variant of Guinevere?)
But I think this is terribly far fetched because I can't quite imagine how some English movement prior to the OTL War of the Roses, or emerging in some ATL variation of that conflict, could result in a strongly anti-High Church faction that could plausibly rule in Britain and suppress connections with the Roman church, which by default would fill the place an Arthurian cult would fill if somehow or other Britain could be held apart from the Continent successfully repressing all attempts at Catholicism hanging on. What would be the ideological basis of such a movement? With monarchs like Henry VIII and Elizabeth being arbiters of what doctrines would be set to rule the Established Church, I cannot see them failing to be shrewd enough to offer the masses something quite close to Catholicism but under their control; this would preempt the development of the Arthur mythos unless the ATL *Tudor-analogs deliberately decided to introduce Arthurian elements, and I think they would face far too much sincere and serious scholarly criticism on the more radical reformist side to get away with such a thing; it would be denounced as a crass and cynical paganism even worse that Popish to try that I think. Anyway when I look at Courtly Romance I find it hard to see as something more amenable to a Protestant than Catholic viewpoint; at best it falls in neutral common ground--but tending toward everything Puritans protested.
So, someone had better be more audacious than I can manage to be in envisioning this. It can't emerge in deeply medieval conditions due to the affinity to the already ruling upper classes and lack of grassroots among the English peasantry, and by the time those form at last, the whole ambiance is too old-fashioned to survive except as part of a larger Catholic allegiance that represses its greatest potentials.
Really it is already so influential I don't know we could take it farther.
