Your chromosomes define your gender
No they don't, which is demonstrated by the existence of trans people. Chromosomes are a genetic indicator of an individual's sex. They have absolutely nothing to do with gender whatsoever.
they set your biological gender
This is not something that exists. There is no such thing as 'biological gender'.
which alters your hormones
No, that would be your endocrine system.
which affects your behaviors.
Nope, that is demonstrably false. Trans men, for example, act differently to cis women, even though both groups share the same chromosomal makeup.
A transgender individual is one in which these messages become confused Chromosomes can't become 'confused', and we have absolutely no definitive evidence of why trans people are trans. In addition, the sex chromosomes of trans people are coded with the same information as in cis people. You're mistaken. Culture merely defines the rules around these behaviors, otherwise no person born male and raised male would want to become "female"
Culture does not define rules about behaviors, because behaviors aren't evidenced in chromosomal makeup. Culture CONSTRUCTS gender roles and gender stereotypes, which have no basis in human physiology and are arbitrarily modified and adapted over time. So you're wrong about this, too.
As to the bathroom issue that's exactly it, is it really fair to say to the majority "Yes we know "she" has a fully functional penis but "she" says "she's" a woman so they can use the female toilet, no matter how you feel".
Yes, it is absolutely fair to say such a thing. The prejudices of cis people aren't a valid reason to enforce discrimination against trans people, any more than the prejudices of white supremacists would validate segregating people of color from public amenities. Restricting bathroom access to trans people is a violation of the Civil Rights Act.
Or is it better to have an "other" toilet so that isn't an issue Yeah, we could have separate shops, restaurants, restrooms, train carriages, drinking fountains, schools... Segregation is in no way problematic or harmful. Oh, wait.
no confusion if the passport says "shemale" and the individual has both breasts and a penis.
One, 'shemale' is a slur, not a gender identity, two, the federal government is not in the habit of labelling people with slurs on official documents, three, not all trans women have a penis (and not all cis women have breasts, for that matter).
Thank you for reiterating your bigoted views.