Yes, no statues prohibit British royals from marrying foreign nationals or non-Christians.
Princes in Britain's royal family have married foreign nationals for centuries; to cite a few examples, these include the following well-remembered queen consorts: Eleanor of Aquitaine, wife of Henry II; Catherine of Aragon, first wife of Henry VIII; Charlotte, wife of George III; and Mary of Teck, wife of George V. Indeed, marrying foreign princesses was the norm until the 20th-century, or rather the marriage of Albert, Duke of York (later George VI), to Lady Elizabeth Bowes-Lyon was the first instance of a Royal who succeeded to the throne marrying a British subject since James II.
The Act of Settlement (1701) prohibits the succession of a Roman Catholic to the British throne, so marrying a Roman Catholic who didn't convert to the Church of England would at present disallow any children from succeeding to the British throne; however, no statue prohibits the marriage to a non-Christian.
P, S. Problems, however, might result in a marriage of mixed faiths:
---Hinduism doesn't prohibit inter-religious marriages, but Islam does.
---Islamic law considers the husband the head of the family and therefore doesn't allow a Muslim woman to marry a non-Muslim husband.
---The children of a Jewish woman are technically considered Jews, and if a child of this marriage were to succeed to the throne if might be difficult for him or her to be the Supreme Governor of the Anglican Church.
---Buddhists can marry non-Buddhists, but it is also recommended that a Buddhist marries only someone who shares his or her world view.
---How could an atheist or agnostic be the "Defender of the faith" ?
---Scientology? British courts have called it "pernicious nonsense".