With regards to using gender-neutral pronouns in general, it's easy if most of the people I talk to are keen on doing the same, but if I am talking to someone who uses gendered pronouns I will "echo" -- for instance, I say "Kylei went to the store" and someone says, "did he write a list?" I'll respond with "no, he's not quite that organized," even though if I am rambling about Kylei I almost never use gendered pronouns. I can stop myself if I am very careful, or if I have had little contact with gender-specific-speakers for the past few days, but the echoing is MUCH harder to stop than general references.
Anyway, I now have a "front name" which starts gender conversations much more often than pronoun use would, so that reason for "ze" is gone. Also, unobtrusively removing gender references and not 'correcting' people's assumptions often leads to them being surprised when they realize their assumption was off, and I feel like that moment of surprise is pretty much the most useful stereotype-breaker. I don't think the actual conversation about gender-neutral pronouns is that helpful.
More importantly, people tend to interpret "ze" not as a lack of reference to gender but as a reference to a third kind of gender, and so feel that if I refer to them as "ze" I am assigning them a gender. I can explain my intent, but not to everyone, and when I refer to trans people I worry that my hearers are assuming I'm "othering" them, putting them in a different category from cis people. Even though it is absolutely not my intent, and not the meaning of the word, the idea that I might be perceived as approving a cissexist attitude is very worrisome to me. I try to compensate by outing myself and critiquing cissexism whenever I have the chance, but I'd rather just not risk it. "They" does not have that othering connotation. Cis people use it to refer to cis people whenever they don't want to refer to gender or when they don't know it. I still dislike the grammatical awkwardness of "they" but as someone on my twitter list pointed out, choosing grammar over people is problematic: so I have decided to try and change.
In my journal and in papers I will retain "ze": in my journal my reasons are listed plainly and in papers I do not want to get marks taken off for bad grammar (and I still am unsatisfied at the idea that a singular "they" should be treated as a plural "they" with regard to verbs). In casual conversation (such as other internet spaces and in-person conversations) I will try to use "they." I know I will fail along the way and my language may be stilted sometimes but I know I'm capable, eventually, and I'll get there.
Dance for Your Reflection