The problem is, it's not really about gender, it's about appearance (which is still wrong).
Most people are tribalistic in nature. They will seek out people who are like them or make them feel comfortable. Step one is be attractive and step two is don't not be attractive. If someone is trans and passable (to the point where the interviewer can't even tell) then they're getting the job.
Likewise there are also rules about, no piercings, no tattoos, nice clothes (either from a t-shirt and jeans to a full on suit depending on if one is cleaning tables or a CEO). The difference is you can't sue over these rules.
That said I imagine it's still super hard for trans people to find work. This also depends on skill level too (where if you have enough skills it doesn't matter what you look like as they'll deal with you because you're the best option.) But they still don't want you interacting with the public at all. With trans people it's because people think "oh it's a guy in women's clothes and that makes me feel weird" and that not only will they get less sales but that people will go shop elsewhere in order to avoid seeing them.
We are super lucky to live in such a liberal area as this. We at least have a few opportunities here, and things are only getting better/more accepting. In some other more rural areas... well good fucking luck. Shit, in at least one state just being able to use the fucking bathroom is an issue (and another state is trying to pass similar legislation.)
To me, it all comes back to companies should hire those who are most qualified, period. The best person for the job should do that job no matter who they are or what they look like.