Regardless of what the English people think,
That should be ‘British’ people, actually. For better or worse, the monarch is titular head of England, Scotland, Wales and Northern Ireland. Or the United Kingdom of Great Britain and Northern Ireland, as it should be called (but isn’t very often).
there are apparently laws on the books that would give persons in certain quarters
Um, who would these people be?
the means to force parliment to act
I think parliament probably would act, but only to rush through a law that permitted a monarch to be Roman Catholic. Provision would have to be made for the headship of the Anglican Church, and that would mean either the role passing to another royal, or the disestablishment of the church, neither of which would cause any real consequences to anyone.
regardless of general public opinion - or lack thereof.
Parliament only ever does things because of public opinion - after all, its made up of politicians and fellow travellers (and a few hereditary peers of waning significance). That’s why they’d rapidly pass a new law, because public opinion would be (overwhelmingly) that religion isn’t a relevant issue when it pertains to who gets to wave imperiously at us at film premieres and other events for the tourists.
And believe me - these people would indeed act.
They might try (it would help if I knew who they were so as to be able to comment in greater depth

) but the nation and its politicians wouldn’t care enough to listen to them.
To the posters who spoke regarding the hatred of Catholics in the UK: I don’t experience this, and as a religious who wears a habit I think I’d be a fairly good target if people were looking for one.
There is some contempt for religion generally, sure; and perhaps the high profile abuse cases have made the church more of a target than usual in recent years; but the virulent hatred of Catholics that is sometimes found in non-Catholic countries is the province of only a small minority here. There are similar small minorities who exhibit prejudices based on race and other issues, but typically the UK doesn’t do hatred very well. It takes more energy than we’re willing to put into anything.
