I bet he wouldn't date or have sex with a transwoman. Easy for blokes to say TWAW but they would never actually live by it because they know transwomen aren't actually women.
Families can disagree bitterly on all sorts of issues. Most people haven't thought through the implications and aren't aware of the realities of such issues because they have only ever read media sources that push a very positive, rosy picture. It makes it easy to jump to knee jerk reactions and slurs.
It's upsetting to hear your husband say these things, but for many people it takes a while for them to change their mind. Many of us started from the position of what's the harm, be kind, only bigots would be opposed and so on. But over time, doubts and questions can start to make an impact.
Avoid the topic as much as possible. It's tempting to want to discuss all of it in depth, but it can put people off. Find an angle that is most likely to appeal to your husband and focus on that. For most men, the sports angle is the easiest to understand. So forget about all the other stuff for now and maybe once in a while mention something about sports.
Sometimes it's really effective to focus on tangential topics. Talk about how hard women have worked to gain their own sports. Talk about the physical and biological differences between men and women. Have you seen the picture of the British swimmers at the Olympics? The men and women were side by side and the sex differences were amazing. All were elite athletes but the men's bodies and women's bodies were so different.
Also the video of the Olympic relay race that had mixed sex runners. All teams except one started with a female runner and finished with a male runner. But the one team decided to start with a male runner and finish with a female runner. The results were amazing. As expected at the start, the team with the male runner was way ahead of the women and the woman on his team was ahead of the men runners. But in the second half of the race, the men caught up so quickly and the woman was left trailing behind. Really profound example of the differences in male and female bodies.
Little things here and there. Agree to disagree for now and avoid getting into arguments. Lightly touch on topics that stimulate questions.
Maybe even order the new Testosterone book and suggest your husband reads it. It has nothing to do with trans issues, although it briefly touches on it as part of the effects on hormones on the body. That might be a better angle to start with as it isn't focused on trans people but rather the physical differences between women and men in general.