Where by "specifically Nazi" you mean "the parts that gjm doesn't approve off". [...] Speak for yourself. I very much don't approve of point 20 from their program. "The state is to be responsible for a fundamental reconstruction of our whole national education program" is a nice-ish sounding way of saying, "we will ram whatever propaganda we want down all kids' thoughts and force you to pay for it".

No, I think that's not the why. I think the actual why is because the Nazis lost the last war and so became known as the incarnation of pure evil, and everything they touched turned to pure evil, the end. In less flowery prose, "Nazi" (or neo-nazi) nowadays is just a derogatory term without much historical meaning. I am not a fan of NSDAP and though I don't know much about Golden Dawn I doubt they are a bunch of decent fellows. If someone calls them neo-nazis, I mentally translate it to "I don't really like 'em". But if people want to insist that they are actually, literally Nazis and pine for the good old days of the Third Reich, well, at this point I feel compelled to point out that no, taking derogatories literally is rarely a good idea.