She’s Jewish. The law was changed in 2012, they can marry Roman Catholics, but the royal can’t convert and still ascend to the throne. As head of the Church of England the monarch must be Anglican.
Every site that I have found that says she is Jewish sites a quote from her in an article called “The Jews in ‘Suits’” where she supposedly says she is Jewish. But she describes herself as a New York Jew even though every other story about her describes her as growing up in Los Angeles.
So I tracked down that article and found that the quote in question is from the author of the piece, not Markle. She wasn’t interviewed in the story and isn’t even mentioned except in a caption of a cast photo from the series “Suits.”