Antidisestablishmentarianism... It's real.
The British Act of Settlement, was passed waaaaaay back in 1701, and propped up against an indignant Scotland through various forms of skullduggery a few years later. It dictates that only Protestants who are not married to Catholics can succeed to the English Crown (and, therefore, the British Crown). It's still in effect, as is the policy that the Church of England, a Protestant sect, is the official state church. Each pretty much mandates the other, as the monarch of the State of England is also considered to be the head of the Church.
Needless to say, a lot of people think that this is pretty fucked-up. The concept of separation of church and state is certainly not present in this governmental system, no matter how nominal the monarch's secular powers might be. The people who oppose the whole thing, (disestablishmentarians) think that the Church of England should be stripped of such a privileged position.
At the same time, however, if one is going to have an unelected monarch (figurehead or otherwise), it's going to be a difficult thing to justify in a supposedly democratic society without some sponsorship by a higher power. As it would be utterly impossible to receive the blessings of every religion for a given single-faith sovereign, one is forced to either choose one church, or create one specifically for the task. The latter option was long ago chosen in England, a decision strongly defended by followers of the philosophy of Antidisestablishmentarianism.
People are still fighting about this.