Shane Sutton is a sexist? Burn the witch!
Joking aside, I think people should take a step back here before there is another repeat of the disgraceful Tim Hunt saga.
Yes, Sutton is known for not worrying too much about appeasing the 'PC' thought police, as when he said that Wiggins 'couldn't pull the foreskin of a rice pudding'. Doubtless, he also drives his riders hard and expects no back-chat from them. As Varnish herself has said "Don’t get me wrong, the boys don’t get it easy."
However, Varnish also seems to have a mouth that is rather too big for her own good. When I have ridden at Manchester the whole place reeks of corporate control-freakery, and speaking out against the management in such an environment is a cardinal sin.
Also, we don't know the full back-story, how Varnish's performances compared with the rest of the team, how well she fitted in to the team structure and so on. Yes, her speaking out might have played a role, but then again malcontents are often seen as being potentially fatal in a team situation.
OK, so she is understandably angry, but by accusing Sutton of the most universal and unanswerable of crimes, 'sexism', knowing that in this day and age most institutions are so terrified of the twitter mob that such accusations are often enough to end someone's career, irrespective of how valid they are, her going to the press and so on, does suggest that the underlying problem is that she simply isn't the sort of 'professional team player' that the likes of British Cycling expect their riders to be. (Or unquestioning corporate clones, to look at it another way.)
She has made her grievances personal, and that is rarely a constructive thing to do.