I, too, performed sometimes sober sometimes not for many years. My regular venue got used to me "taking time off" from alcohol, and even though I haven't had a drink since 2013 I still get offered drinks. For the bar help it's their job to offer drinks. For others it's showing affection, so it doesn't bother me.
One thing that helps is I started placing a quart thermos and a tea cup on my amp right next to me, and between songs people - even drunk people - notice I'm drinking tea. This tends to minimize the offering of drinks from the audience. I just tell the bar I'm not drinking alcohol before I start to play, or when they ask I tell them a pint of water no ice would be fantastic.
I thought folks would bug me more about it because they've known me for marathon shows that start out set one pretty controlled and sober for the early crowd, and the after midnight sets would be humorous drunken freak fests. The drunks liked it. The relatively sober would leave. Now, though, I can do the marathon and late night I get loose and do lots of the same material, but MUCH better and with more precision and energy.
I usually perform solo or with one other musician (who drinks and smokes weed moderately), so I would imagine if you play in a band that's accepting drinks it could be a little harder. Then again, most people won't even notice if you leave drinks alone or hand them to someone else.
So, my plan has been to decide on a drink of choice and stick with it. It used to be beer when I performed with the rule of no whiskey til midnight. Now, I bring my own tea and drink only club soda or seltzer from the bar. Have a plan and stick to it.