Yes, bad things sometimes happen to people because of some group they in some sense belong to. Or other ways in which their commonality gives them an interest in common.
However, that often does not mean they see eye to eye on what the cause or remedy is. Or very often, even what the problem is.
This is just as true of women's groups. Many see themselves, honestly enough, of representing the best interests of women. But actually, plenty of women differ in how they see their interests.
So when a woman's group says that something is a problem, or advocates a policy position, whose interest are they actually representing?
They are actually representing the women who agree with them, while denying the validity of the viewpoint of those who disagree.
There was a time when many of the successful identarian lobbies tended to be very limited in policy demands, and often they were on very concrete things, because they avoided making pronouncements on things that were highly controversial in their membership. That's no longer the case though. (Incidentally, it's true of other lobby groups to, Amnesty International is a good example.)