I think you have to keep in mind that you are employees of an establishment that makes money by selling drinks. So, saying “I don’t drink” could seem a bit hipocrical. Said another way, you are being party poopers in a place that’s there for people to party. So, I’m not saying you should drink if it’s not your thing, but, also be aware that that can seem rude to people who are buzzed and are buying you drinks as a show of appreciation.
I have to laugh a bit. Way back in the early 70's when I was in a touring nightclub group, we would typically play 4-set nights, 5-nights a week, 50-weeks a year. As part of our regular routine, during our 10-minute breaks, we would go out and sit at different tables during the night. That way we could meet a lot of people, give them a little bit of I "I know a guy in the band" status, and invariably we would get offered drinks.
4-drinks a night wasn't bad, but we would sometimes play military clubs (NCO clubs, O-clubs, etc.) and they always bought you two drinks at a time primarily because on base, they were cheap and drinking was primarily what they did in their off-time. Whereas 4 drinks a night is fine, 8 drinks a night would get me more than a little buzzed and my playing got sloppy, which drove me nuts.
After a couple of nights, I came up with a solution. First thing I would do would be go to the bar and ask for a non-alcoholic Bloody Mary. Then I would tell the bar tender to please serve me that same thing when anyone else ordered it for me. It was my "usual" and when offered a drink, I'd often say, "just tell the bartender I'd like my usual". And Voila', I'd get a non-alcoholic Bloody Mary (tomato juice with spices and a celery stick); I could still play fine all night; and my kind host would feel magnanimous because he bought me a drink.
This worked well because the music sounded good (no drunks on stage) and the people we met one night would often bring their friends back a couple of times to see us that week and impress them that he knew us. Plus, I got to meet a lot of nice folks doing that.
So no need to be rude, just be prepared. Make the Bloody Mary your drink of choice with a little help from the barkeep. A Tequila Sunrise can also be passed off as real when it's not. A single malt whisky can't and neither can shots. Just don't do shots...