The gender wars, don't need to call it that, have much to do with grammar, especially around pronouns. I'm familiar with pronoun battles as it is, given how often a speaker assumes the "we inclusive" i.e. including me in some "we" that I either (a) fight or (b) have nothing to do with or (c) maybe have huge respect for but do not consider myself a member of, and so on. However that "we" stuff is a two way street as I learn new ways to use "we" on my side as well.
Nor is it like I'm in any way alone in my appreciation for pronoun battles. The "we" fight, as in "what 'we' white man" is pretty dang old, hence that phrase.
In progressive Portland, Oregon, early 21st century, it's considered polite in some circles (circles I've been in, with people I know personally and appreciate as individuals as well as members of various other circles), especially in a work setting with strangers, to introduce oneself and the pronoun one prefers, the prevalent choices being she, he and they. That's right, a 3rd person plural is more gender neutral and so becomes idiomatically singular.
Individuals with a background in show business are far more accustomed to the idea of a persona, a role, a character. One needs a home base for one's avatar, a person to be in daily life, and then, with that as an anchor, one swings out into various alternative roles, professionally, as an actor / actress (assuming a determinate sex or gender for the character, not always the case, especially in cartoon voice parts where gender may be deliberately ambiguous).
Portland is big enough to attract a theatrical crowd i.e. we have enough readers, theater-goers, music fans, film addicts or whatever, such that separation of persona and avatar has come to seem natural, so if your DNA sex is XX yet you're more yourself, persona-wise, being a male, then the pronoun should go to your character, not to your "horse" ("dog") or physical "piece" (body). Ditto if you're operating an XY, apparatus-wise, but feel home-based in a female persona, then it's the persona that gets the pronoun.
The person's self-declared orientation is accepted and the pronoun goes with the persona. Ergo, in polite society referring to a person as "he" or "him" who is biologically (DNA-wise) not male is grammatically accepted. By many. We might accept it, your group might not.
Just to go into the anthropology a little more, these people who identify with a gender other than their gender at birth are considered "trans" whereas those identifying with their birth gender (i.e. decision as to sex at birth or pre-birth) are considered "cis".
Should it come up whether a sister or friend is a cis-woman, that's meaningful to ask, though may not be polite company discussion in the Victorian sense. Inquiring directly about DNA or one's "cis-or-trans-ness" is quite possibly somewhat intrusive as "does this relationship involve community policing of some kind?" ("What? Are you a cop?" -- "cop" as in "officious busy-body" i.e. a "need to know" person with a perhaps self-assumed right to pry). A trans-woman was most likely cis-male at birth if this grammar is followed.
Helpful in this connection is the mnemonic GLTBQQI, sometimes with L first. The final "I" is for inter-sexed and refers to bell curve phenomena wherein sex is biologically ambiguous at birth, issues of persona aside. The more clinical term might be "hermaphroditic" but that comes with cultural baggage. "Inter-sexed" is not synonymous with "uni-sexed" and "androgynous" though these are all related concepts.
"Asexual" and/or "gender-neutral" are in many ways fixed points of reference regardless of one's personal orientation or persona, but of course we're into "eye of the beholder" country. People come calibrated differently, which is somewhat the point / cause / driver of the gender wars in the first place. "War" as in "tug-o-war" maybe: it's played out in grammar as the battlefield, is semantic in nature.
Obviously in busy street life you do not always have time to learn a person's preferred pronoun and they may dress ambiguously, and in those situations polite society accepts a shared but more rude public space wherein pronouns often fall into the wrong places, and a kind of jarring occurs, as when riding a bus or subway (metaphorically).
People use the wrong pronoun with you, about you, making wrong assumptions or not obeying the rules of grammar you're used to given your ethnicity as a Portlander. We have lots of tourists after all.
Speaking of public spaces and miss-assumptions, gender-typing public restrooms is an age-old architectural feature and gender-queer learn to bend their characters sometimes. Many a trans-male has a fallback or secondary fem character when needed and vice versa. Gender-neutral restrooms are already the norm where a small coffee shop or restaurant has only one shared public toilet. Turning two gender-biased restrooms into two gender-neutral is just a matter of changing signs on the door in some cases (not others -- plumbing also an issue).