Do you have the dna of a male or female after the surgery. Do you have a uterus, ovaries, real vagina? Can you lactate? Do you have periods? Can you become pregnant? If all , or a majority, of those are no, you are not a female.
No but you don't make other women too uncomfortable plus you can't rape them or get a hard on without a dick.
Who cares about DNA if the physical appearance and brain waves match (from a locker room point of view, otherwise there's another discussion about this in L&R).
Even in Iran you're fully considered a woman if you go through the whole process. Cis-genderism is enforced though.
Out of curiosity, those that are using the "transgender person with male genitals cannot go into a gendered facility for women because this person might be sexually attracted to that gender" argument, have you thought about how your logic applies to gay (yet cisgender) people?
if you make this argument then we could make gender-neutral locker rooms for everybody since the girls are going to be abused by lesbians anyway. Or 52 locker rooms to accomodate every possible situation.
In reality gays are just a few and they're discrete.
Also this being not a prison, someone subduing a male and doing gay butt rape is unlikely.
Now if you make gender-neutral locker rooms, the risk of abuse increases.
I guess it's a matter of statistics. It's really unlikely that a gang of gay rapists takes over a gym shower.
A gang of heterosexual molesters is much more likely.