> I'll hazard an analogy: if I refuse to debate certain people on the Internet who don't adhere to my rhetorical standards, am I "imposing my regime on everyone else" (and thus I should be required to debate everyone who wants to debate me)?

Yes, you’re forcing them to abide by your “rhetorical standards”. The point of debate to help someone see your point of view. Nowhere does it require abiding by a certain process. If so, one could make the argument that only those that have not taken logic and learned the proper way to debate can engage in such things. So yes, you’re forcing people to play by your rules, or you refuse to play. It’s actually quite a bit childish.