Hey, I have to look at you, and you make me want to puke. What can I do about that? 
well, all I want to do is to be permitted to leave whenever I see a transgender co-worker
so: you have my permission to leave!
Well, if you can demonstrate that you consistently cannot control your stomach when you see this coworker, and are not malingering, I see no reason that they should not accommodate you.
OTOH, if you mean it figuratively, then you don't need a court decree to take care of the situation. Just leave, as you suggest. Quit. Find another job with coworkers you can stand.
Of course, if a transgender person joins that job, too, then you can quit that one also. Just keep leaving jobs until you find one you can tolerate.
It seems pretty silly, but if that's the life you want to live, it's a free country.
Heck, feel free to move to Russia or Iran if you'd like. I'm sure they don't have such problems. You have all sorts of options.
The only option you don't have is to force your petty morality/religion on another person. Not in this country.
