From THE TELEGRAPH:
Nick Clegg, the Deputy Prime Minister, began work towards repealing the 1701 Act of Settlement, under which heirs to the throne must renounce their claim on marrying a Roman Catholic, in order to introduce full equality between the faiths. However, the plan to abolish the Act of Settlement was quietly shelved after the Church raised significant objections centring on the British sovereign’s dual role as Supreme Governor.
Church leaders expressed concern that if a future heir to the throne married a Roman Catholic, their children would be required by canon law to be brought up in that faith. This would result in the constitutionally problematic situation whereby the Supreme Governor of the Church of England was a Roman Catholic, and so ultimately answerable to a separate sovereign leader, the Pope, and the Vatican. There is no similar prohibition on the Royal family marrying members of other faiths such as Islam and Judaism, or those who are openly agnostic or atheist.
COMMENT: Unless we remove the role of head of state from the monarchy then a Roman Catholic can never be allowed to be our monarch for the reasons the Church of England states and for the one other very important reason. Our head of state has to sign all acts of parliament before they actually become law. This is, at present, a symbolic act as convention (and the threat of the abolition of the monarchy) dictates that the monarch signs everything. But this is powerful symbolism for the British because it makes the point that politicians are subject to a non-politician. As our monarch is regarded as the person who represents all the citizens of Britain this means that politicians are subject to all of us. It's also, in theory, the last resort for stopping our government from becomming despotic. However, if the monarch was a Roman Catholic and our government passed a law stating that lesbians could have an abortion up to nine months of pregnancy, a Roman Catholic monarch could not sign that act without being excommunicated from their church. For the sake of that hypothetical Roman catholic monarch a Roman catholic should never be put into that position. For the sake of our monarchy, a Roman catholic cannot be allowed to be put into that position because if such a monarch was to refuse to sign such legislation because of her or his faith, then there would be a constitutional crisis that could only end in the abolition of the monarchy.