Something I have noticed is that a lot of people don't really understand that the symbols represent ideologies on the opposite ends of the political spectrum.
When we were in high school, my boyfriend went through a phase with one of his friends where they would wear ushankas with sickle and hammer pins on them. Then our peers would joke with/make fun of them and call them Nazis...
I think the two get conflated because they both bring to mind oppressive dictators and have the general connotation of radicalism, which young people sometimes cling to without really understanding the views themselves or the history behind it in their quest for a unique identity.
I'm not sure if this applies to E/D though. They both seemed smart enough to know what each symbol referred to, but I'm not sure what their actual political beliefs were, and I suppose I wouldn't be too surprised to find out that Eric leaned more right and Dylan more left. However, I don't think Eric put much thought into whether his views matched those of the Nazis. I think, like Sabratha said, he and Dylan used the symbols for dramatic effect to seem more evil and intimidating, because Swastikas are instantly taboo.
As for Eric's apparent antisemitism based on his reaction to Dylan, I think it has more to do with playing the part than any real beliefs he may have held.