I see nothing wrong with supremacist From Lexico:
supremacist: A person who believes that a particular group, especially one determined by race, religion, or sex, is superior and should therefore dominate society.
If you drop "especially one determined by race, religion, or sex" -- which is not essential to the definition -- you have "a person who believes that a particular group is superior and should therefore dominate society." This is exactly the sort of person you've described in your question. If you want to talk about a particular type of supremacist, i.e., member of a group that believes itself superior or supreme, you need an adjective, e.g., white supremacist, black supremacist, female supremacist, etc.