... what happens if a future monarch decides to convert to Islam or Bhuddism? ...
They would have to abdicate the King/Queen of England has to be a Protestant.
Not just any Protestant, the Monarch must be a legitimate Protestant descendant of Sophia of Hanover and must, in addition, be in Communion with the Church of England, that is a Confirmed Member of the Church of England (Not Scotland or Ireland, sorry) and must swear to preserve the established Church of England and the established Church of Scotland. The Sovereign must also promise to uphold the Protestant succession.
Room for modernisation there, I feel...