I don't like nightclubs because they are loud and I don't find that I connect with people well. There was a time in my life when I liked going out dancing but I don't really like it anymore. I'm finding myself wondering though if dancing would be fun again someday.
Anyway even when I was drinking I would tell people I don't like nightclubs but I do like them, the person who invited me. Point being if someone invites me it's because they like me and think they would enjoy my company and I want to make sure they know that I'm rejecting the night club and not their company. People are understanding and if they aren't it's because they don't want my company, they just want to party and are looking for someone to reinforce the activity.
There's nothing wrong with saying "you might find this hard to believe lol but I have social anxiety and I also don't drink so nightclubs aren't really my scene. I'm really glad you invited me because I'd love to hang out sometime but believe me you don't want to see me in a nightclub!" It's true, you're not lying, and you're not rejecting them. You could, if you want, invite them to a different, less triggering (of social anxiety and of drinking) activity and see if they are down.
Best to find out now if they are looking for a collection of people to party with or real actual friends.