It will if he's one who believes he's the only one with the right to be armed. It will if he uses it as an excuse to restrain me without cause or if he believes he has the right to even temporarily take it from me. And being compelled to answer violates my right to remain silent.
Any LEO who believes any of the things you posit would find he's wrong [and unemployed] after you sue him and win, because he would definitely be wrong.
As for your right to remain silent, that applies only if and when you have been accused of a crime, not anywhere, anytime you object to being asked a question.