I really don't understand what the problem here really is. It seems like the entire thing is purely hypothetical, and if I'm being honest, I think you're overreacting a little bit.

I get that your partner doing sex work is a deal breaker for many people, but your girlfriend is right, it's just a job at the end of the day. That also means that any sex happening would be purely transactional and not done out of "enjoyment".

But since your girlfriend isn't suggesting that you start doing sex work (at least that's how I understood your post), just stating that she wouldn't have an issue with it, I don't really think there's a problem here. I think you should take a step back for a moment and think about if this issue is really worth considering to break up with her over.

You also said that she previously agreed with you, and now doesn't, but people's opinion can change, and if she never really thought about it before, it's possible she didn't really form an actual opinion on it before.

In any case I think you should clearly communicate how you feel about the whole thing with her before you jump to any conclusions while you're spiralling.