You talk of being tired of a particular line of argument, in defense of shutting up all arguments for a particular idea. If you're tired of a particular idea, to the point of wanting to shut it out from being argued for (even in novel ways), that's called being anti-free-speech.

Have you, in fact, listened to an argumentative speech on one of those questions, or others you feel this way about? Not even counting whether some new guy could have something new to say, can you honestly be said to have heard the full-length intelligent argument for the position and found the evidence lacking? Or is there nothing being 'moved on' from at all?