I certainly wouldn't put Crass in with the Oi bands.
After the 76 punk revolution was "bought up, cleaned up, souped up" by the music industry, the emerging post-punk (not to be confused with New Wave and subsequent punk-influenced movements) tended to be marginalised and split into factions.
It was the emergence of so-called Anarcho-punk and associated / derived splinters. Though Crass were against labelling, they would possibly fit best in this genre.
The Oi ! bands were something different altogether. Proudly Working Class, they entered the world punching, kicking and screaming, took a share of what was left of punk, gave it skin-head-appeal and a right-wing agenda, and revelled in the ensuing chaos.
Crass were vehemently against this promotion of racism and class through punk. Check out the lyrics to "The Greatest Working Class Rip-Off" from Christ - The Album";
"Ain't it just a rip-off? Oi Oi Oi !
What a f--ing rip-off, Oi, Oi, Oi !.....
.....Punk attacked the barriers of colour, class, and creed
But look at how it is right now, do you really think you're freed?
Punk once stood for freedom, not violence, greed, and hate
Punk's got nothing to do with what you're trying to create.
Anarchy, violence, chaos? You mindless f**king jerks.
Can't you see you're talking about the way the system works?"
[cont.]