Thats an interesting post though not sure Brexit has anything to do with culture wars, more like good old fashioned greed.
In the case of the majority of voters, not culture war related.
But I would guess that a minority of the voters (large enough to change the result if they voted remain or not bother to vote), chose to vote leave, not partcularly because of the EU, but more as a Trumpite F*** You to the establishment.
So now you're going back to the 1690s not the 1950s...
Wasn't the English reformation mainly because Henry VIII wanted a divorce? And didn't it lead to centuries of antagonism between Protestants and Catholics? Neither seems a good precedent for a policy in modern times.
In the 1530's there were many among the senior ranks of England's government and great and good who agreed with Luther and his protestant reformation that was underway in Germany, you might call them leavers, and there was a lot of popular support among ordinary people for luthers ideas in parts of England that are now most "Brexity" like Essex. Said ideas were circulating in pamphlets printed on then newly invented printing presses.
However, Henry V111 was a fanatically religious catholic and hardline authoritarian who burnt any he caught for heresy and had been declared "Defender of the Faith" by the pope for a tract he wrote putting the boot into Luther and co, so they largely kept their heads down.
Rome's decision in the annulment fiasco (it had been expected to be an uncontroverial rubber stamp exercise for "sound" biblical reasons) went down in much the same way as the European Court decison on prisoners votes did.
This allowed the "leavers" to persuade Henry that Rome was corrupt and the only way to save the souls of England was to declare himself as effectively an emperor and effectively pontifex maximus in the English Church (a title the Pope appropriated from Ceasar when the western Roman empire collapsed).
So Henry was to lead a "Herstigte" (means purified in Afrikaans) Catholic Church, free from the laxity and corruption of the Church in Europe. His leaver advisors had very different intentions, but doctrinally Henry was a fanatical catholic and would have burned alive anyone advocating Lutheran (protestant) doctrines.
Instead they waited until he died and they could sieze power as "regents" for his under age son, upon which in came the english text Book of Common Prayer and the real presence of Christ in holy communion was dismissed as superstition.
For this the senior "leavers" involved all got burned alive for heresy when the young King died after a short reign and Henrys fiercely remainer (Catholic) daughter Mary Tudor, who had married the King of Spain took power and declared England Catholic again
She then died and was replaced with the Leaver protestant Elizabeth, who although excomminicated by the Pope, kept certain catholic elements in the English Church (like Bishops) to try and keep everyone happy. Tbis was unsuccessful with a century of stife, "terrorism" and civil war until the Glorious Revolution in 1690s banned Catholic Kings and mandated that "no foreign prince or potentate shall have any power in this free Realm of England" (the strife continued pretty well unabated to this day in Ireland though).
This settlement lasted from 1690 until the UK joined the EEC in 1973, handing all sorts of powers to the modern equivalent of "foreign princes and potentates", thus reopening all the old wounds of 1536 to 1690 again and, in the last few years, brought us closer to civil war than anything since then.