The high tide of fascist skinheads was really 78 - '81. The Rock Against Rascism concerts (Sham 69 involvement) and anti -fascist movements such as the Anti-Nazi League bascially killed off the neo-nazi National Front. Later the acid house and rave culture supplanted the football hooliganism which fed into fascist skinhead culture and thus ended it (ecstacy fuelled love and inclusive partying). But yes skinhead does NOT equal fascist.
Sorry, that should have been Sue Townsend. My brain temporarily stopped working!
Also if you are trying to research 'how the skinheads went from nice people who just wanted to accept everyone - to be related to violent racists' you might find it is a bit more complicated!
Cartainly the early skinheads were influenced by Jamaican music and culture and were failry tolerant in many respects. But I don't think they were ever entirely cute and cuddly. I think you might find it was a working class outsider movement that was always prone to extreme politics and a certain level of violence.
Politically far-right skinheads probably only became the dominant faction during the eighties but I'm pretty sure they existed before that period. Likewise, although they aren't common anymore there are still ska-loving far-left anti-racist skinheads surviving to this day. I saw plenty when I went to see 'the Specials' not long ago.
The shift was probably a reaction to the harsh conservative politics of the time - as well as Asian immigration and mass unemployment. There was increased violence and nastiness at many levels of society - it was certainly a bleak time for football fans such as myself.