Re: the far right thing. That has not been my experience, no.
I wouldn't be surprised if it could become that, as the far right-ers and fascists tend to co-opt leftist movements for their own. i.e. skinheads, oi music, and the like.
As far as spirituality is concerned, I always got the impression that most people into straight edge were either atheist or agnostic. Not really big fans of any sort of organized religion.
Don't know anything about sexuality or sexual activity. Mostly it was about being opposed to corrupting your body with substances, as opposed to sex.