OK, so here's where things get a little stale and sticky.
Historically, heirs to the throne can't marry a Catholic due to The Act of Settlement, a document enacted in 1701 by the British Parliament. This law, passed during a period when Protestants feared widespread Catholicism, states that only Protestant heirs of Princess Sophia, granddaughter of James I, should be permitted to take the British throne. Later, the law extended to Scotland.
The law still exists today, forbidding Catholics or those who marry a Catholic from becoming a member of British royalty. Even though Anglicanism and Catholicism are similar, if the bride-to-be is Catholic, she must convert to Anglicanism to become part of the royal family.
Only two years ago, Canadian-born Autumn Kelly, a commoner, converted from Catholicism to the Anglican church before marrying Peter Phillips, son of Princess Anne. Prince Peter would have been forced to give up his place in line to the throne if Autumn refused to denounce her Roman Catholic faith.
It's hard to imagine that today's multi-faith society still upholds this law, especially since it doesn't prohibit any other religious person from joining the royal family. Even though it would be a huge undertaking for members of legislation, they're currently reviewing the contents of The Act of Settlement and considering doing away with the discriminatory law altogether. Maybe one day, the system will expunge the act and be open to allowing spouses of British royalty to freely practice whatever religion they choose.