The Act of Settlement does two things, according to an expert in Crown law I consulted via email in London.
(1) It prohibits anyone other than a lineal descendant of Electress Sophia of the House of Hanover from becoming monarch; (2) It prohibits a Roman Catholic Sovereign or a Roman Catholic consort; (3) It grants Parliament the right to disqualify, remove or amend the succession to the throne at any time for any reason.
Regarding a formal renounciation of rights, I was told this is not possible. As noted by others, marrying a Catholic automatically disbars you from the succession under the Act. If you were Sovereign, Parliament would pass an Act of Abdication to remove you and your descendants from the throne for becoming Catholic.
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