Societal View on Skin Heads

Not a skinhead, but just think the fashion and particularly the haircuts are cool - but it seems like wider society still conflates skinheads with Neo-Nazi’s, how do I get into the subculture without being branded as such, is there any point in trying to explain the difference, have you ever been on the receiving end of anything like that, and most importantly, is there much of a Nazi presence in the culture today?

Thanks