The fallacy is thinking that "This is the same thing as Hitler's genocide" is a fact, not an opinion.
No, that's not a fallacy. In fact, your description is a fallacy in itself: you are distorting analogies and misunderstanding their function.
When analogies are proffered as rebuttals they are typically intended to challenge some implied premise. Analogies, however, are not meant to compare two or more things as though they're similar in
every respect. (Otherwise they wouldn't be analogies; they'd be
identities.) They're meant to compare two or more things that are similar
in some relevant respect(s). No analogy should be rejected simply because one has found a mere dissimilarity—one must reflect on whether or not the dissimilarity was central to the point.
The point of referencing Hitler or Nazis in a properly constructed analogy isn't to say that the other thing that's being compared is "just like" Hitler or the Nazis. It's invoked because it's a variable we can all get behind (that Hitler and Nazis are
bad) while exposing the flaw in the
structure of an argument (what distinguishes an argument's
validity as opposed to its soundness).
Consider the following exchanges:
Theistic Person: My religion teaches that same-sex marriage is wrong.
Gay Rights Advocate: Some people's religions teach that interracial marriage is wrong.
Theistic Person: So you're saying opposing same-sex marriage is just like racism?!
Gay Rights Advocate: Acting on my homosexual feelings is morally acceptable because I was born this way.
Theistic Person: Psychopaths and alcoholics were probably born that way too.
Gay Rights Advocate: So you're saying being gay is just like being a psycho or an alcoholic?!
Take the first exchange: Gay Rights Advocate didn't say opposing same-sex marriage is "just like" racism. Rather, he used the analogy to interracial marriage as a counterexample to the implied premise that "Whatever a religion teaches is right." Gay Rights Advocate appears to be saying that referencing religion doesn't exempt a view from moral scrutiny.
Likewise in the second exchange, Theistic Person isn't saying psychopaths and alcoholics are "just like" being gay (or even behaving gay, for that matter). Rather, he used the analogy as a counterexample to Gay Rights Advocate's implied premise that if people are born with a certain disposition, any behavior driven by it must be morally acceptable as well.