My sister-in-law refuses to come to Thanksgiving because of my guest's pronouns. How do I avoid further conflict?

Hi all! I'm a huge fan of this subreddit and the podcast. I've never posted here before but I do really think I need an outside perspective here.

I (27NB) live with my parents in the northeast US, and my two older brothers (Let's call them "Drake" (30M) and "Alex" (36M)) are coming up from the midwest/southern state that they live in. They're both supposed to be bringing their girlfriends. Drake is engaged to a girl we'll call Theresa (30ishF), and Alex is dating but will soon be engaged to a girl we'll call Sadie (25ishF). For context, I've never met Sadie, and I've only met Theresa once, but it was at a big family dinner like two years ago where we barely talked. My family generally is also very conservative and religious, though I'm personally neither.

Now, onto the conflict. I'm also inviting my friend that we'll call Sam (35NB). They've been going through a really rough time this year and don't really have any family, but they're one of my best friends and I didn't want them to spend a holiday alone. I texted my brothers last Friday just to say basically, "My friend is joining us for Thanksgiving. They use they/them pronouns, and I don't really care what your opinions are on it, I expect you to please be respectful." Completely reasonable, right? Alex texts back saying that's fine, and I never get a response from Drake.

So imagine my surprise when my mother asks me the next day what exactly I told my brothers. I tell her exactly what I told the boys, and she explains to me that Drake had called her and said that Theresa no longer wanted to come. My mom says that when she pressed Drake on why, Theresa had said that she'd apparently had a "bad experience" before and didn't feel comfortable anymore. Mom continued to press him on it, thinking maybe she'd had a conflict with someone at work or something over their pronouns, but it wasn't even that. Literally all it was was that Theresa had gotten into an argument ONLINE, and was now deciding that my friend, who she does not know anything about other than their pronouns, is not someone she wants to be around.

For what it's worth, my very conservative Christian, Texas-born mother defended me and Sam and told my brother straight up that Theresa didn't have to come if she didn't want to, and that it was her house and she had the final say in who is invited. I'm a bit shocked because I guess I always assumed that if something like this ever happened, my parents would throw me under the bus. I suppose Southern hospitality wins out over transphobia in her mind?

I guess I'm just wondering how to proceed. I haven't talked to Drake at all about it, because I have nothing nice or good to say to him or his fiancee at all. I don't want it to turn into further conflict, but he's absolutely the type to resent me for making his fiancee feel unwelcome or something like that. I also feel a bit of disdain for him since we're both full-grown adults and he felt the need to go crying to our mother about this instead of talking to me directly if he had a problem. I don't really talk to my brothers outside of family gatherings, but we still have to deal with each other so I don't want this to be the start of a lifelong grudge.

I'm sorry if this is long-winded. If you have any questions or need further info, please let me know and I'll do my best. Thank you in advance.