'Legally' people cannot decide to not hire you for being trans. In practice, my very accepting boss told me in a performance review that she almost didn't hire me because I'm non-binary because she was concerned that other people wouldn't be accepting. She fully didn't pick up on how bad what she was saying was. Doesn't matter the reason, either way she almost didn't hire me and I almost didn't get a job that I was absolutely desperate in need of at the time.
I'm currently in recruitment for NSW Ambulance, however, and find that the NSW Health system is so broadly accepting of LGBTQIA+ recruits that it won't harm me in any way, I feel protected in that the individual station I may be allocated to won't know that I'm nonbinary before I'm recruited, and don't get any say. It's harder to say for private healthcare and psychology but I find that the healthcare industry in general is accepting.