They're all "trans." At the very least, that makes them somewhat related. Simply insisting they're not is not a good enough argument.
As for respect, again, the exact same thing can be said for transsexualism. Anti-trans people still insist that "literally impossible for you to become a man/woman" if you aren't born into that sex. There are plenty of "casually" transphobic people who say similar things. "If you want to dress up like a lady and call yourself a 'woman,' fine, whatever, but don't expect me to go along with your delusions; as far as I'm concerned you're still just a man in a lady's dress."
You're right in that this has absolutely nothing to do with sexual preferences. As to transgender people, they do share the commonality of being "trans."
In the end, these are all labels that are socially constructed. How we define sex, gender, species, or what animal you are are all social constructs. Thus ultimately none of it is a tangible reality, meaning that with enough social pressure, our way of thinking about it can completely change.
Welcome to the age of identity politics.
That's the same thing people said about changing your sex/gender, or about gay marriage. They were "literal impossibilities" because of how those things were defined. Over time, those definitions changed, social attitudes shifted, and now not only are they possible, it's an offense to deny that they are.