As far as I know, for all they suck, Wal-Mart doesn't discriminate much if at all. In Canada at least. Here they're commonly known as THE employer who'll hire just anyone. If X place won't hire you, Wal-Mart will. Obeses, gays, (maybe trans people but there's only one Wal-Mart and not many trans people where I live), elderly people and whatever visible minority you can think of, they hire them. Not so long ago, there was a trans woman from this forum who was having a very hard time finding a job considering her weight and trouble passing, but Wal-Mart hired her.
As for the warehouse... Dunno. Not like I can know them. What I do know though is that even though in job search I'm pretty sure there's a fair amount of discrimination, it'll happen less often than people think that people who are already settled into a job will get fired for transitioning, really. You'd need a boss who is especially an ass, and willing to find fake excuses to put someone out of a job for such a motive. It does happen, but I don't think (or rather I hope) I'm overly optimistic when I say it's unlikely.
Also, I feel sorry for you. That sucks a lot. Next time you rent an apartment, make sure everyone is on the lease, so no one can do such a thing. :/