The weakness, and it is a weakness, of the generally liberal discussion participant is that they very often want to discuss what a thing is and what it means. Wonkishness is a positive trait in discussing policy, but it means that rhetoric, no matter how openly disingenuous, has to be addressed; the consequences (or the inanity) have to be dissected, that's part of why they are there.
Incidentally, this is what leads to the current state of affairs--the side that is unmoored from any pretense of reality can say whatever the hell they want and will put the other side into knots.
It isn't clever, and it is frustrating because your advice is good, but it is real.
These days, I'd probably just not respond to bad faith communication, but I've historically enjoyed being horrible. Unlike a politician, you don't have to preserve your own credibility in the eyes of onlookers, so you can just be awful if you want.
I find that there is usually a fairly small number of "gotcha" questions that come up over and over for a particular topic. the "trans people in competitive sports" question in this thread is a good example. what makes these types of questions rhetorically effective is that they're usually at least half-rooted in truth. in my experience it's more effective to recognize the likely gotchas and have a response ready, or better yet, preempt it entirely. at the very least, you should explain why you're not answering the question, lest it appear that you are the one arguing in bad faith. you have to keep in mind that you're not just trying to convince your interlocutor but also your audience.
A good politician would never answer that question. Instead they would answer a different question that they already had a good answer to. “I think the important thing to remember here is...”
This tactic works just as well online. Never directly answer a question you don’t like. Always stay on message.
By the time you finish your answer the listener should have already forgotten the question.