Is responding to a statement that free speech should not be compromised with, "so Hitler had a right to say what he said?" be a form of question fallacy?

I am a novice when it comes to logic and rhetoric, and am looking for some insight.

If someone argued that, "Free speech is a fundamental principle that should not be compromised," would someone asking, "so Hitler the had right to say the things he said?" be considered a form of question fallacy?

It seems the questioner is forcing their opponate to either admit they are wrong, or side with Hitler.. although from what I've read about loaded and complex question fallacy, it doesn't seem to apply.

It seems the question itself isn't fallacious, but the intended effect is to have the audience come to the fallacious conclusion that supporting free speech = supporting Hitler.

Does this fall under any definition of fallacy?

No fallacy, defending free speech would not be a fallacy and if someone concludes that by answering "yes Hitler has a right to free speech" that that's an endorsement of Hitler, then they would be committing the fallacy.

One could argue the Ad Hitlerum fallacy—attempting to make it seem as if you are supporting Hitler. There is also an implied false analogy as you suggest—associating supporting free speech with supporting Hitler.