The only place this will be an issue is in a culture where "rounds" are bought - for example, UK drinking culture.
In the US, everyone buys and pays for themselves. In the UK, at least where you go up to a bar to order (not in restaurants etc), it's normal that one person takes everyone's drinks order and goes to the bar to buy a round for everyone in the group. With large groups, this can get super expensive very fast, and if there're only a few rounds, not everyone gets to buy a round each time people go out. Instead, there's usually an informal method of remembering who's paid for rounds most recently.
It gets more complicated because some people get cheap drinks, others sit out a round, others get super-expensive fancy-pants drinks, others drink soft drinks or even water: to simplify things, each of these is counted as "a drink" regardless.
In these cultures, when you're asked what you want, you say "just a coke, please" or "nothing this round, thanks". When it's your turn to buy a round, (you can tell by people saying "it's your round" and looking at you expectantly) you bite the bullet, take everyone's order, and buy the drinks, and don't kick up any kind of a fuss about it. Some people make a game of trying to dodge their rounds, hitting the bathroom when they see people's glasses getting empty and such. Don't be that guy.
UK drinking culture is one of the things I'm very glad to have left behind by moving to the US, where instead it seems there's an eating culture, where everyone goes out for a meal together, and not drinking is the norm because you have to drive to get anywhere.
UK drink culture involves far too many drunk people yelling at each other over loud music for my tastes. It's got a bit less unbearable since smoking indoors was banned, but still not the way I'd rather spend my evenings. So I'd usually stay for a couple of rounds then make my excuses and leave - I was usually not the only one, either.
If some immature CEO or similar tries to press you to drink, it's considered OK and even admirable by almost everyone to say "No thanks, I'm driving" or just "No thanks, I don't drink". Generally people don't press into the "why"; the assumption is that you'd have said why if you felt they needed to know.
If they do ask why, pretty much any reason is acceptable and will be respected, whether it's religious, "doctor's orders", or something else. Only the response "personal preference" could be taken by some as being judgemental and affecting "team fit". If it is taken that way, then yes, it's a poor team fit, and you might want to find a better team, because you probably wouldn't want to fit with that team.