I like to think of these people as directionless edgelords who appropriate Nazi symbolism because the attention that they get from it feeds their egos, not due to any sense of patriotism. I'm sure there are those who genuinely believe this stuff, but like the OP said, many are probably trolls who take this stuff way too far.
Hmm... I honestly think that's far too generous an explanation and gives people too much credit.
If I may power-level a-tad, I watched a member of my family's general Third Reich military romanticism grow over time into genuine Nazi-esque thinking. It started with regaling me with how great the Fallschirmjäger were, because he'd been a paratrooper and felt some-kind of kinship, and before you knew it he had JewWatch.com in his bookmarks. He was a mark for this kind of thing, always had been I guess.
Maybe that makes me biased but I genuinely think just writing this up to "edge-lording" is a mistake. But these people do believe this stuff I think, it takes more than just wanting to be a troll to declare some-kind of sympathy for the Third Reich and genuinely talk about exterminating sub-humans. When I'm at work and see something on the news and call the Spanish a genetically evil race, we all know I'm just joking or impolititely voicing concerns at the Spanish government. That's a bit of edge-lording.
These people aren't generally just edge-lording, and I think it's a genuine case of convincing yourself into racism. I've watched the gradual introduction of Nazi sympathiser dialogue. He'd tell me, indignantly, how these Waffen SS who dressed in US uniforms were all killed as spies and how it's be a war-crime if it had been the other way around (I think he was talking about Operation Greif"). Maybe that would be true, but the only reason you'd get indignant, or even really know about this in like 2013 or what-ever, is if your a Nazi Sympathiser looking for acceptable grievances. Of-course Dresden, the 9/11 of Neo-Nazis, was eventually brought-out. It was when he was condemning the French Resistance for killing poor young German Soldiers ("They'd have been called terrorists if it was the other way around", he'd say) that I finally knew he'd lost the plot. You could almost make a check-list of the Neo-Nazi arguments he'd read on forums and was just repeating.
TLDR. Don't underestimate how much this ideology can genuinely have an effect on people. The Swastika is a powerful symbol and Nazism a powerful ideology that almost rewrote an entire culture in just a few years. I'll be honest, when I was younger, and more like the previously mentioned family-member, I'll say write now that maybe I strayed close to the edge of thinking like that. Don't now obviously. It's insane. White Nationalism is insane. But I'm still staggered by how this invented symbolism gripped an entire country and some people take that to the next-level. There's a certain kind of person that this stuff just appeals too. I know that first-hand, it's why I'm really critical of these people, Alt-Righters and White Nationalists even though I'm actually something of a conservative patriot myself - because I know where it goes.
Getting a tattoo or something is edgy to a lot of people, advocating Nazism goes beyond that.
