LGBTQ+

I'm wondering if the person who called OP not a real woman was coming from a similar place to drunk and angry you.

Most charitably, she probably thinks it's okay to call what she thinks are "pick me" women "not real women," because according to her you can never arrive at that opinion unless your worldview is unduly influenced by trying to please men, unless you are actively trying to come off as "on the men's side" so that some man sees you say that and rates you a little higher in his "dateable or not" scale. No real woman with non-man-pleasing motivations would ever disagree with her on that topic unless the woman was actively trying to get picked by a man. Dismiss all disagreement by namecalling them as "not a real woman."

Or she probably thinks that having (what she sees as) an extremely harmful opinion justifies hurting the other because hurting them teaches them not to have bad opinions... somehow.... Having a "pick me" opinion means your entire gender is fake because non-trans women would never ever once have the Bad Opinion, and trans women are "fake" women who don't have the Real Lifetime Gender Experience to arrive at the One True Good Opinion.

That ain't it. We don't misgender awful cis people, so why are we doing it to trans people? The answer is "to hurt," but it also has the extra effect of "if you step out of line your identity is no longer valid, trans acceptance is entirely conditional on always having the perfect opinion, otherwise we'll whip you back into shape with some prime invalidation." Of making onlooking trans people doubt whether they're really accepted, whether they pulled out the invalidation to be hurtful and they still are for trans rights, or if they pulled it out because they genuinely think you can't be trans but are willing to pretend for the nice people and go mask-off when sufficiently angered.