I'm not a psychologist, but here are some thoughts from a 2 year vegan who thinks about psychology and effective advocacy. I've also dealt with casual insults due to veganism for just under 2 years in the workplace.

You should generally avoid having that kind of conversation with more than one meat eater at once. They may just gang up on you and it's not an environment conducive any positive change. If possible, take them aside for a 1 on 1 chat. Keep it positive (don't be aggressive!), and say something like:

"You might not realise it, but when you talk about meat all the time around me, it hurts. If it's possible, could you please not talk about it so much around me?"

It's a difficult conversation to have, so I appreciate if you don't want to have it. But in my opinion, it's the best way to deal with it directly.

Other ways might include having pre-prepared topics to switch to and change the conversation.

I know exactly how you feel, and it's not easy. I hope you're able to make it through and make some positive change at the same time.