The British monarchy has rules governing who may sit on the throne and what they may and may not do; and there is no possibility that Diana could have influenced William and/or Harry to convert to islam because she had a relationship with a muslim, and then for either of them to take the throne. None.
Similarly to the way that our President is Commander-in-Chief of the military, one of the centuries-long established duties of the British sovereign is to be “Defender of the Faith”, meaning the Anglican Church of England.
The British sovereign is not allowed to marry a Catholic, for instance. It would take an act of Parliament for such a marriage to take place, and likewise for a King or Queen to convert to another religion than Church of England. Even when Charles married Camilla, they were not allowed to marry in the Church of England because they were both divorced, and thus had a civil ceremony.
In other words, UK isn’t California.
Would certainly hope so, since the Brits have OUR missiles on their submarines.