Perhaps, but if this is the case 'real' trans people are 0.00001% of the population.

I disagree with the exact %, but yes, it's an extremely low percentage, absolutely.

The vast. vast majority of cross dressers were not going to kill themselves if they didn't get to cut off their dick. This phenomenon is a meme that has been planted in the mind of people through ideologues/psychologists and then spread in the population, like hysteria in the late 19th century, or multiple personality disorder in the 70s/80s.

Crossdressing has nothing to do with trans people, but yeah, of course they shouldn't be treated like trans people? They're both related to sex, but one is a mental issue, the other one is just a hobby/interest or whatever it is.

Do you think people were just killing themselves left and right when no viable surgery to look like the opposite sex was available?

Literally yes, why wouldn't they?

Were third genders (in cultures that had them)

There weren't any real third genders, most "third genders" are just a subservient eunuch class, this is leftie bullshit.