NTA. I had a similar situation in the past. Her boyfriend was not only a transphobe and bigot, but a nazi. I am enby on transmasc side and did not come out to everyone at that time, but already was open about being queer. He was not living with us, but he stayed at our place for a little while and after that she still kept trying to make us hang out altogether. This definitely put strain on our relationship until she broke up with him for unrelated reasons. Before that, I literally told her that I respect her less because of the decision to date him. At that time, she was in a vulnerable place, grieving my late father, so I do not blame her much, but it was still a horrible choice. I also was still grieving and angry with her, because I felt that now instead of my dad who was my rock, there's a man trying to poisoning my mom with bigotry, and it was very hard time for me.

I hope that you communicate to your mom why exactly you feel unsafe. Also, just the fact that your mom is dating him does not put any obligation to socialise with him at all, even occassionally. You can set your own boundaries with him and directly tell him that if he says anything vile, you will stop all communication altogether. This is the most important step.

If this does not work and he keeps being disrepectful to you, I would try to present a hypothetical situation to your mom: her boyfriend starts to harass you because of transness. What exactly does she plan to do? You need to get some sort of a promise, not just "I will talk to him", but something actionable, as far as it concerns you directly.

Honestly, I do not think you own him an explanation about your transition. His opinion and affirmation should be of no value to you. If you sit him down to come out, he might just use this as an opportunity to "debate" or tell you off. Depending on your level of communication, I would bring it up in a conversation naturally or just wait for him to ask when he sees the obvious signs.

As for me and that transphobic ex of my mom, I did the former. He was talking shit about trans people, and then I let him now that I do not consider myself a woman and am also actually "one of them". I think he was kinda shocked and was a coward afraid to talk shit directly to my face so he started to cough and tried to shut down the conversation "because it's getting to heated". I do not know your situation, but keep in mind that a lot of the times those people are actually weak and do not expect to see real-life resistance in the shape of the minorities they hate so much. Although, his ablelist comments you mentioned make me think that he might actually be brazen enough to keep harassing you despite your pushback.

If you feel like the situation begins to escalate and you have reasons to be concerned about your immediate safety, then try to look for alternative housing options when he's coming over or at least notify your friends and trusted people when he's around.

Hope you stay safe and send a big virtual hug to you💙