It's not a false analogy; you're just focusing on a difference which isn't relevant to the analogy. Yes, there is arguably a difference in how people should treat people with face tattoos, vs trans people. But the analogy isn't about how employers should act. It's about how they do act.

The purpose of the face tattoo thought experiment is to help you understand what a trans person has to deal with in practice.

The point is not that face tattooed people shouldn't have a hard time getting a job. The point is that transsexual people have a /harder/ time, and that this is clear evidence that transsexuals can't just go and get a job as a waitress, shopping mall sweeper, store attendant, cashier, "you name it" as sergiotapia proposes.

Then the point was made poorly. Again, I was responding to the bit about face tattoos.

There are trans people (e.g. me) that consider transitioning is a choice. no more different than choosing toyoya vs Porsche

Ok fine, then you made a choice. If it's a choice then you have to be an adult and deal with the consequences.