A bit of an orthogonal argument: the problem isn't Nazis per se, it's what Nazis believed. Treating the idea of Nazis as too serious to make fun of and treating the idea of making fun of Nazis as a noble goal both have the fallacy that the thing we're saying "Never again" to is people with swastikas and straight-arm salutes. Now, yes, there were a few of those people at Charlottesville. But there are a lot more people who have the same ideology as Nazis - that ethnic minorities are the cause of the ethnic majority's economic anxiety, that a special police force to put ethnic minorities in concentration camps is totally fine as long as there are valid laws supporting that, that local opposition to this police force is illegitimate and treasonous, that the sexually "deviant" are ruining the integrity of our culture, that we have more of a duty to the well-being of our own race than to the survival of other races, etc. - without having any of the visible trappings of Nazis. The more that we say that the thing we object to (either by avoidance or reappropriation) is "Nazis," the more we make room for people with the same beliefs to prosper under different names.

(Side argument: putting the focus on "Nazis" also seems to invent distance between the man on the street in 1930s Germany, who just wanted a good life for his family, a prosperous economy for his country, and success for his nation's troops, and us in our own countries today, because that man lived in Nazi Germany and voted for the Nazi Party. It explains away the fact that an entire country like any other Western country suddenly went along with the Nazi agenda because that country was, somehow, full of Nazis, who are, somehow, different from us.)

I have seen lots of people make the argument that "Nazi" is a bad descriptor for anti-Muslim beliefs/policies that closely resemble historic Nazi anti-Jewish policies, because they're anti-Muslim and not anti-Jewish. (Usually this comes with some sort of argument about "Judeo-Christian values," or about how Islam is different, or something - and when I point out that the same sorts of attitudes were prevalent at the time against Jews and Judaism, they seem to think it's an answer that those people were wrong and they're right.) I think that's a sign that we've failed badly to teach "Never again" in a meaningful way, in a way that realizes that the problem is not to make sure it's never 1930s Germany again - of course it never will be. It will be somewhere else, someplace else, and some other people.