This should be the top-voted comment of the whole thread. I used to teach history; it makes me roll my eyes when I hear comparisons between Nazi Germany and the current moment. It reflects both a lack of historical familiarity with the unique circumstances of Germany in the 1920s and 30s (including recently losing a world war), and also, as you say, a lack of knowledge of other more relevant historical examples — of which I’d also put Erdoğan at the top. It’s just a conversation-stopper and a rhetorical cudgel rather than a serious attempt at historical contextualization.

Surely the Venn diagram needs not be a circle for you to draw parallels, nor does the existence of a more direct comparison make other comparisons moot.

Surely the fact that the current ruling party has an influential faction who explicitly reference Nazi Germany as an ideal worth striving for is relevant to setting the current moment in historical context. Yes we're not LITERALLY Nazi Germany for a variety of reasons but that doesn't mean it doesn't paint a picture of what they want to do, regardless of how successful they will be or what that will look like in practice.

Personally I think the most apt historical comparison is the Fourth Crusade and the Sack of Constantinople, but since we don't LITERALLY live in the Middle Ages and have ethnic divisions between Greeks and Latins one might say that's not a relevant comparison either.