I hope I've understood your question. I think it's worth noting that often, in the context of an argument, a question is meant to be another way of phrasing an objection. For example, suppose I say "How can your theory account for x, y, and z?". Sometimes what I'm really saying is "Your theory *cannot* account for x, y, and z." I might follow this up with arguments for why x, y, and z are inconsistent with or unexplained by your theory. Other times, I may lazily leave it at the initial question and hope that you understand intuitively why I think x, y, and z are at odds with your theory. Anyways...

Suppose we are objecting to some proposition, P, by asking a hypothetical question. More precisely what we're doing is describing a hypothetical state of affairs that is difficult or impossible to account for given the truth of P. And when P is a theory or proposition that is supposed to be necessary in scope, then it should be able to account for these hypothetical states of affairs. If there is even one possible state of affairs that negates P, P cannot be necessarily true. Philosophers invoke thought experiments in metaphysics, epistemology, ethics, etc. for this purpose all the time, since the theories in these areas of philosophy are often intended to be universally and necessarily true.

Here's an example. Suppose you say "all ravens are black". I can't just say "there's a possible state of affairs where there is a non-black raven", and conclude your proposition is false; my hypothetical state of affairs is irrelevant to the truth of your statement. On the other hand, if you say "it's morally correct that people should act to maximize the greatest amount of happiness for greatest number of people", I might likewise object by conjuring up some ridiculous-sounding situation, a thought experiment, where someone acting in such a way is doing something clearly immoral. This *would be* an acceptable objection. The difference is, with the moral proposition it is (as I understand it) intended to be a proposition about how *all people* ought to behave *in all circumstances* that they *might* find themselves in, whatever it may be. It has some kind of modal force.

If I've understood you correctly, then to answer the actual question in your first paragraph, I think the first thing you should do when debating is to always phrase your objections as *declarative statements*, not as questions. If your interlocutor still claims something like "I refuse to respond to any objection that makes use of hypothetical situations", you should state exactly what it is that your hypothetical situation is meant to contradict. If their statement has any sort of modal force or consequence, then hypothetical states of affairs are fair use.