Lots of discussion points here, but let me address two or three in particular:
blatant Nazism hurts their legitimacy in the eyes of the public
Nope. No, it really doesn't. Trump was never a legitimate contender from his opponents' perspective (due to dirty foreign money) and his true believers would stand buy him as he ate a live baby on TV.
Take a look at some approval polls that show he still has significant support from Americans. (Likewise with Musk, likewise with DOGE.)
Second point: It doesn't matter. He doesn't NEED legitimacy or approval any more. He's in power, Musk is at his right hand, and the two of them are acting with complete impunity. Seriously, they should both be hauled off in chains and tried for treason, not to mention hate crimes and hundreds of less-sexy crimes. But they're not, and so it just doesn't fucking matter.
Thirdly, where did it come from? We're discovering now that the Christian hard-right has been carefully staging this for HALF A CENTURY! Since not long after Roe v. Wade, they have been laying the groundwork for what Project 2025 is carrying out right now: A ruthless coup backed by religious extremists and foreign opponents. The Heritage Foundation was founded in 1973. PNAC was founded in 1997. And there are more.
Fundamentally, Trump's first term was to see how much they could get away with. When they lost the 2020 election, the Nazis spent four years purging the party of unfaithful (i.e. people with either thoughts or morals, or maybe even both), then won last year, and were finally able to remove their veil: The government no longer needs the will of the people to execute their extremist plans.