Not unless the law was overturned. What is amazing to me is the blatant religious bigotry that exists in the UK. What if the monarch wasn’t even a Christian? If William became a Buddhist would he have to renounce his right?
If the heir to the throne were to convert, this would provoke a constitutional crisis. The 1997 European Convention on Human Rights, which is incorporated into UK law because we are members of the European Union, guarantees everybody freedom of religion and freedom to marry who they want (Denmark recently had some trouble with this as a right-wing government tried to outlaw inter-racial marriages). The Act of Settlement of 1788 states that the King or heir to the throne cannot be a Catholic and cannot marry a Catholic. UK law usually recognises the more recent law as being the more correct, so the monarch probably could be a Catholic.
Of course, at the same time, it could be argued that the office of King was a job/vocation, just as someone who is a Catholic priest would cease to be a priest if they converted to Islam, and forfeit their parochial house, income, etc. likewise the country
could sack the King. The question would be
who would sack the King, and on what authority? Parliament? The Church of England? In reality, most people today wouldn’t give a fig whether the King was a Catholic, with the possible exception of the Northern Irish. Frankly, the personal power of the monarchy is non-existent, nobody cares, and the current heir to the throne has no interest in leading (or following) the Church of England - he is married outside the church and wants to drop the title of ‘Defender of the Faith’ and change it to ‘defender of faiths’ reflecting multi-cultural Britian.
In theory, the Prime Minister cannot be a Catholic because the Prime Minister is responsible for appointing the Archbishop of Canterbury. In reality, Tony Blair doesn’t make this decision personally, there is a commission of Anglican clergy that reports to him and he rubber-stamps their decision. During 2001-2003 the Leader of the Opposition, Iain Duncan-Smith, who would have become Prime Minister if he won a general election, was a Catholic, and he was a Conservative. I’m sure the ‘old guard’ of the Conservative party would have known if he could not legally have been PM, and would have blocked him from leading the party if that was the case.
The monarchy will continue to draw American tourists, who will continue to pay us lots of money to see some soldiers marching around in silly furry hats, irrespective of what religion the King or Queen might be. That, after all, is what they’re there for!
It is an unfortunate anachronism that the CofE is still an established church and the vast majority would like to see it disestablished (along with the ejection of the CofE bishops from the House of Lords 
)
- congratulations to Mr Blair. I’m not really bothered, just like, I daresay, most of the British population. 
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