Pronouns: I have a gender neutral name for a reason, suckaz, and I resent this question. I am, however, a woman, and I have never doubted it. People who see or know me say she/her. When people don’t see or know me, and assume I may be he/him, I like it. Who doesn’t enjoy changing identities sometimes, not to mention being perceived as a member of the ruling class, and treated like it?
Axé.
coldhearted scientist وداد 
Your first point is excellent. I had not even thought about pronouns as a way of assigning and policing a gender identity, but now that you point it out, it becomes obvious. My name is not gender-neutral but I am sometimes taken by casual onlookers to be male and it is an interesting shift in perspective when that happens. I think we need a broader understanding of what it means to be a woman or a man, not narrow definitions that indicate that if you don’t care for either nail polish or machinery you must be something else. I don’t doubt that there are people who are truly that third thing, but suspect that many “they” pronoun-users just (reasonably) object to the gender stereotypes foisted on them, as if He-Man or She-Woman were the only available options.
The mainstreaming of transgenderism is TOTALLY about assigning and enforcing conservative gender roles and subjecting everyone to the male gaze, and calling it liberating. And yes, many of those I know who use “they” are going it for the reason you suggest.
I think there’s a lot of race/ethnicity policing too, although I don’t find it as pernicious. Still, I get tired of officious white people born yesterday telling me that since I am white, I must think X, or must never have thought of Y.