I'm pretty sure the reason was because red was a striking colour and the flag was designed with the German flag colours under the 2nd Reich. I'd have to look it up but ultimately I don't think it matters. Mike's reasoning years ago was that it was eye catching and they wanted at least 2 colours from the American flag, they just couldn't find a way to make blue work.
This isn't all that accurate either - if you look into it, the nazis effectively designed their ideology to be appealing to people. You can see this in the name - People like Germany and being German, so they were a 'National German' party. At that time, socialist ideas were gathering steam, so they also were a 'Socialist Worker' party. Merge them together, and there you have the party.
The flag is the same way: The Swastika was some kind of cross originally IIRC, and since Christianity was widely adhered to in Germany, they could slot that into their flag. Same goes with the red border which gives socialist vibes, then all the colors next to each other are Black - White - Red, like the old German imperial flag.
In contrast, the NJP from the start was just people wanting to LARP as Hitler, hence why they went for a similar design. It's not trying to appeal to anyone besides themselves.
I agree, it's a toxic subject. People need to understand in politics you need allies, not friends. You have a common foe, you need to push it back. It is okay to otherwise hate each other. Just hate the barbarians at the gate more.
Alt-Right discussions circa 2015-2016 agreed on this, then Trump turned out to be a disappointment. From that point on, everyone who disagreed was always a shill, a fed, a jew, or a CIA psyop derailing the 'moovment'.
You could probably write a university thesis on why the whole thing went tits up, but one of the big ones is that internet shitposters and funnymen aren't fit to be leading anything. It's why every alt right group eventually collapsed in a shitstorm of drama, doxing and pointing fingers that everyone is CIA.
It's funny looking back, really.