Australian social services are, in my experience, really good about this sort of thing, unless there’s a reason your details have to match up with your passport or whatever.
When I got my SA teaching registration, I filled in Mx on my forms, and the well-meaning lady at the desk who didn’t know any better said my “Ms” was unclear and had me refill it. I was nervous and timid and just went along with it. A few days later, I had to come in to drop off some proof-or-qualification document, and the woman found me, apologised profusely over the misconception, and changed the paperwork mack to Mx then and there right in front of me. (I’m guessing someone in the office filled her in.)
I’ve always been a not-advertising kind of person, so people don’t usually learn my gender unless they ask, and when I was still doing my degree and too timid to insist on NB pronouns I used to go by male ones if anyone did ask. I look unambiguously female, so I don’t get asked that often. In my teaching degree, one of my teachers knew I was trans from an incidental conversation, but I decided not to mention this on my teaching practicums (one of which was to a VERY religious Catholic school) because it obviously wasn’t worth it for a 5-week job; however, halfway through my first prac, I got a call from this teacher (who was my supervising teacher) explaining somewhat apologetically that she may have accidentally outed me to the staff at the school, unaware that I was pretending to be female, and explaining that if the principal wanted to take me out for an apology beer, that was why. The staff at the school were all very nice to me, didn’t do any big-deal apology confrontations, didn’t mention it at all; they merely changed their pronouns when students weren’t around and asked if they should continue to submit my reports under my (feminine) official name or instead use my (masculine) nickname.Â
I can’t speak for randos on the street, but when talking to people representing institutions, I’ve generally encountered very reasonable people who are as willing to respect my identity as they are for binary cis people. Which is a positive sign for our future, I think.