There was recently a thread by another user here who went through a similar situation at work. She hadn't come out yet or socially transitioned, but coworkers found her Facebook and began to gossip about her. She had success working with HR. If your boyfriend enjoys the work that he does, I'd encourage him to reach out to them as soon as he's feeling up to it. They should be able to help his coworkers understand not only his situation, but how their actions have affected him.
Even if he decides that he no longer wants to work in that environment, I think something should be said to HR. Think about any future trans people that may work there. We don't want your boyfriend's situation to be repeated. Allowing his coworkers to continue their behavior implies that their behavior is acceptable. It may not be the most comfortable conversation to have, but it could easily be brought up in a resignation notice or exit interview.
In a lot of ways, I agree with and understand where your boyfriend is coming from. I'm planning on starting over in a few years, and I'm not sure what my reaction would be if my past caught up to me. It's not that I'm ashamed of being trans. I feel like the circumstances of my birth are generally inconsequential, and should be of no importance to anyone that I'm not romantically involved with. The obsession with and objectification of trans people's bodies by cisgender people just boggles my mind.
I'm so sorry that he's going through this, and I hope he finds a resolution to the situation that he is comfortable with. He is very lucky to have you, you seem like a really great partner. My advice would be to remind him that you love him. Take care of him in whatever way he will accept. Offer to go to therapy with him. Offer to speak to work on his behalf if he isn't comfortable doing so. Most of all, just be present. Let him know that you're there.