To blindly answer this question without any historic or political knowledge of the rules governing the royal family, I would guess that that the young lady in question would have to change her religion and convert to Anglican.
For example, when then-Princess Sofia of Greece, raised Greek Orthodox, married then-Prince Juan Carlos of Spain, raised a Roman Catholic, the Queen was married in a Catholic ceremony and while I don't think she gave up her Greek Orthodox religion (please correct me if I am wrong), she agreed to raise any future children as Catholic in order for her children to succeed rights to the throne.
I also believe that similarly Princess Marie-Chantal Miller had to convert to Greek Orthodox from whatever religion she was raised to marry Pavlos. She had to take classes in the church.
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