It's not the entire purpose. That's part of it, the rest is about enabling abusive men to insert themselves into any place that women and girls have separate from men and boys. They won't accept that women have the right to say no. These men have a rapist mindset and the trans movement is their shield and sword.
And so whenever anyone says that transgender groups are reinforcing gender norms I kind of have to shake my head, because it's difficult to find a group more obsessed with the idea of stereotypical gender norms than the supposedly "gender critical" crowd. And unsurprisingly, that leads to a lot of reinforcement of toxic gender stereotypes; both in the idea of men as an intrinsically, biologically distrustworthy group, and in the practical reality that they are constantly looking at other women and thinking, "is this person a spy, is this person a man in disguise, is this person feminine enough that I can trust them."
And it's just so omnipresent. The above is a comment by someone who looked at a thread about whether or not transgender communities reinforce gender norms, where both sides are reasonably trying to be compassionate, and they could have tried to present a picture of terfs as anything other than what I described them as above, they could have tried to dispute my characterization of gender critical communities -- but they just couldn't help themselves, they couldn't stop themselves from jumping into the conversation and claiming out of nowhere that transgender people all have "a rapist mindset."
So yeah, if you're gender non-conforming, or you don't like gender stereotypes, or you're pushing away from a socially defined set of rules for gender, unsurprisingly, the communities that accept you as you are are all going to be healthier for your development than the communities that are constantly one "she looks too muscular" take away from calling you a rapist.
And it's helpful that whenever I try to explain this to people and they seem doubtful, a terf will literally register a new account just to jump in and prove my point for me <3