heavily based on a tootstorm by Monster Girl Noëlle: 
I hear a lot of people (mostly apologists) complaining about Nazi-punching on the grounds that non-Nazis might get punched too, that "the real Nazis died out in 1945", etc. This is concern trolling on its face, but let's talk about Naziism just for the record.
The group we think of as the post-Weimar German Nazi Party was called the Nationalsozialistische Deutsche Arbeiterpartei, or NSDAP. I'll refer to it as NSDAP to identify it specifically, because otherwise it would be easy to get tangled up.
This next bit is a little simplistic, but it gets the gist across...
NSDAP was predicated on racism, and specifically nationalistic racism. They wanted "Germany for Germans"; the blonde blue-eyed Aryan was their ideal, but not their litmus test.
As such, they had three goals: putting business back into the hands of the German people, expelling foreigners and expanding German control, and maintaining the purity of the German people through eugenics.
The first was Volksgemeinschaft, or "people's community"; it advocated profit-sharing and common ownership of businesses. (It's important to note that this WASN'T Marxist socialism; NSDAP supported the middle class and was vehemently anti-Communist.) The idea was to keep international interests out of Germany, and specifically Jewish interests; NSDAP founder Anton Drexler believed that Jews controlled int'l capitalism and finance. (This formed a basis for their persecution.)
The second was the relatively longstanding German policy of Lebensraum, or "living space". This held that not only was Germany for Germans only, but that Germany had a right to spread out into areas controlled by "lesser races", both for comfort and as a defensive barrier. Lebensraum had provided a pretext for Germany to engage in WWI and it would again in WWII.
Finally, we get to eugenics, which NSDAP argued would "improve the stock of the German people" -- and in the process eliminate those pesky foreigners, of course.
These three ideals - Volksgemeinschaft, Lebensraum, and eugenics - formed the core of the NSDAP's policies and drove its actions. Some of you are looking at this and thinking, "Hm, those look familiar." They do, or they should. Trump was elected on those ideals.
Volksgemeinschaft has its equivalent in "America First". Many of the alt-right hate international business, especially when they think international business is controlled by Jewish people. (When they talk about the Rothschilds, that's what they mean.) When Trump and the alt-right talk about bringing jobs back to the US, they're blaming foreigners for the actions of US corporations.
Volksgemeinschaft is also anti-big-business, which is why businesses catering to people with these beliefs position themselves as being composed of and benefitting the "common people". It's a trick to fool people into thinking they're smaller than they are.
We see Lebensraum in "white nationalism" and immigration bans, but it also manifests in subtler ways. Trump's Wall is Lebensraum, for example.
The appearance of Lebensraum in the US should be no surprise. The US was built on settler colonialism, and it continues today in actions like the DAPL.
Finally, eugenics. It's rare to hear the word these days, since it's so thoroughly entwined with Naziism. But e.g. certain elements of the the anti-vaccination movement are essentially eugenicist (see, as are anti-miscegenation, "conversion camps", etc. Anything that seeks to remove "undesirable" traits from the population is in the eugenics tradition. (see also US/eugenics)
(Note that the eugenics thing is about traits, not beliefs. There's a substantial difference.)
So when we see our President espouse the ideals of "America First", #MuslimBan, and anti-vaxxing... it's hard not to be concerned.
And it's all too easy to look at his supporters, both in the alt-right and closer to the center, and see Germany in 1933 - and we really don't want a repeat of 1938.
There was some additional information from malgranda fantomo (not this toot, which for some reason I bookmarked, and two other users), but although I clearly remember seeing at least one specific link to a 115th Congressional bill about gene-testing, it has slipped through my fingers like sand. ...also, corrected corrections.