Interesting. The GP's usage is aligned with every instance I've encountered over the past 20-odd years (in the U.S.), while the Wikipedia entry appears to have a European focus and is starkly different from my understanding of U.S.-ian denotation and connotation of the term.
See, e.g., Merriam-Webster:
"2: a usually white male belonging to any of various sometimes violent youth gangs whose members have close-shaven hair and often espouse white-supremacist beliefs."
Go to a concert or local show which has music that skinheads like. Find one, and talk to them. They're pretty nice people generally, though they also may be defensive from getting so much shit for being associated with the white power fuckheads. I've heard the european skinheads are a lot more touchy than the american ones.
If they have a patch that says SHARP on it, they are 100% anti-racist, and will probably beat you up if you make a racist joke. A bit violent, yes. But not without reason. Again, not unlike some others (people like Ian MacKaye used to shave their heads and get into fights over stupid personal beliefs and weren't skinheads at all...)
See, e.g., Merriam-Webster: "2: a usually white male belonging to any of various sometimes violent youth gangs whose members have close-shaven hair and often espouse white-supremacist beliefs."
http://www.merriam-webster.com/dictionary/skinhead