I’ve always hated the notion that trans women aren’t “real women” due to different experiences/socialization growing up. Frankly, I think that trans women have a much harder road than those of us who are cis. Not only do you have to deal with being jammed into a role that isn’t who you are, but you have to overcome all sorts of societal prejudices, learn from scratch what gender means, and fight an uphill battle to get the people around you to accept you for who you are. Any male privilege you have growing up is (probably — being a cis woman, I can’t speak to your experience, only sympathize) cancelled out by all that other shit.
The whole point of intersectionalism (IMO) is that we all have different journeys and experiences, none of which make us less or more than other women.