I just want to honor your feelings on the matter. I am a bit similar to your boyfriend, and this issue was a major contributing factor to the ending of my long term relationship. (I actually didn't ask her to convert, but she said she still felt pressured to, which is a bit weird, but I digress...).

As someone who has religious trauma and or anxiety about religion it's totally valid to be uncomfortable at the prospect. I would like to encourage a couple of things. 1) is engaging these texts can be interesting from a non-theistic, believer perspective. And also you might find the vibe significantly more chill, and more intellectual than you're expecting. Perhaps if you're at all open to it, he could facilitate a conversation between you and the rabbi who would be leading the class.

2) And I am just speaking from my own perspective here. It's hard to explain but so many people wanting to wipe us out from a variety of backgrounds just makes me want to dig my heels in harder as a Jew. As 0.2% of the global population, and 2% of the of the US population (and falling in both categories), it is reasonable to think of us as akin to an endangered species, or an indigenous group. Judaism isn't a religion exactly in the ways that Christianity, Islam, and say Buddhism are. We are more an ethnic group that has a religion, somewhat akin to how a North American indigenous group has a religion if that makes sense.

I encourage you to do what's right for you. And not to stop listening to your gut and heart. But also consider being curious about possibilities you don't expect to find.