I thought the split with the Catholic church was precipitated by Henry VIII wanting to divorce one of his wives, an action "condemned" by the Pope at the time. It was this "condemnation" or refusal to accept/recognize the divorce that caused H8 to declare himself head of the Church of England. The subsequent fighting between his daughters and their factions of differing religions was the fallout from H8's decisions and proclamations regarding the Catholic faith, wasn't it?
I like to argue and debate, too, Rascal.
Yes, it's true that the split between the British monarchy (or, more accurately at the time, the English monarchy) began with Henry VIII wanting to divorce his first wife, Catherine of Aragon. Up until this point, there had been Protestants in England, but the monarch had always been Catholic and that had been the official, state religion. However, the Pope wouldn't grant Henry his divorce, so he basically decided to create his own church, the Church of England, and make himself the Head of it. Henry's supporters among the nobility and the court jumped ship with him, and his future children (Elizabeth and Edward) were raised in the Church of England.
However, just because Henry had created a new church and a lot of people had followed him, there was still a significant Catholic party among the nobility and those well-placed in politics. Some of them were Catherine's supporters, some of them felt it was wrong for Henry to go against the Pope, and some just felt it was the most advantageous position to take for various reasons. Anyway, there were a good number of these people, all of whom would prefer to see a Catholic on the throne again.
And Henry's first child, his only child with Catherine, was the Catholic Mary. Much of the political jockeying to remove Mary and Elizabeth from the line of succession and put them back in and take them out again and on and on as it went for quite awhile was based on the fact that Mary was the best chance for another Catholic monarch.
Once Henry's Protestant son Edward was born, it appeared that this wouldn't be an issue, as Edward would likely be followed by all his Protestant descendants. But then Edward took the throne as a young boy and got sick before he had a chance to marry. His obvious heir ought to have been his oldest sister Mary.
But Edward was very passionate about his Protestant faith and did not want the throne falling into the hands of a Catholic. Nor did any of his Protestant counselors, who stood to lose their positions, and perhaps, under the intolerant regimes of the era, also their heads. (At this point there were no rules about the monarch not being Catholic.) After much wrangling, Edward altered the succession so that he would be succeeded by his Protestant cousin Lady Jane Grey. Jane (who is fascinating; I'm writing my senior thesis on her this year, but she's not terribly relevant to this discussion) took the throne for 9 days, giving her the shortest reign in English history. Mary, however, raised an army and defeated Jane's forces, proclaiming herself Queen in London just over a week after Edward's death. There were two more uprisings in the next two years(?) in favor of Jane, but Mary easily crushed both. She went on the earn herself the nickname Bloody Mary for her persecution of Protestants and entered into a highly unpopular marriage with Phillip of Spain, which, had it produced an heir, would have founded a Catholic dynasty. (A great fear in an increasingly Protestant England.)
Of course, after Mary, the Protestant Elizabeth ascended the throne. Yet the Protestant-Catholic tug-of-war over the English throne continued throughout the next few reigns, simply because there were still quite a few Catholics in the line of succession.
This wasn't solved until the 1680s under the reign of James II, a Catholic who was pursuing a number of anti-Protestant policies. The Protestants were relatively calm about all this, because they saw it as temporary since his immediate successor was his daughter Mary who had been raised Protestant. Then James's (second) wife gave birth to a son, who would be Catholic, and panic ensued.
A group of Protestant nobles then invited the Protestant Prince of Orange, William, who had already wanted to marry James's daughter Mary, to come to England and invade. Many of James's Protestant officers defected and joined William's army and James panicked and fled to France. Parliament then declared William and Mary King and Queen and also issued a Bill of Rights and some new restrictions on the monarchy. (All this, and some other unrelated political events, is the Glorious Revolution of 1689.) The new restrictions included the no Catholics rule.
So yes, it did all start with Henry's separation from the Catholic Church, but it took another century and a half before Catholics, and those with Catholic spouses, were barred from the throne, and it was at many times a bloody, messy 150 years.
So while there's no real reason today that the monarch can't be Catholic, there are solid historical reasons for the law. And since the monarchy is so based in history and tradition, I don't think historical traditions ought to be altered unless there's a very compelling reason for doing so, and I don't think there is one right now.