I think you're conflating trans people with drag queens & cross dressers, but your broader reasoning is why there is strong distinction between sex and gender in the trans community.

Trans people know they aren't ever going to be biologically the same, but it's not about the sex, it's about the gender and feeling a certain way. Yes, they present themselves as a collection of traits which you may call stereotypes, but how is that different from any other human? We choose how we act and express ourselves. Your femininity is expressed one way and their vision of femininity is another, but just like how you wouldn't hate or condemn a goth/hysterictomy'd/childfree/etc woman for expressing their femininity their way, why not let trans people do the same? Them being who they are doesn't really affect biological women any more than any other subset of women would.

Also like other subgroup, there are attention seekers drawn to the label and go overboard with the pronouns, etc., but just ignore them as you would any other attention seeker.