Wine in ancient Greece was well liked and a lot of people definitely drank it. There was a Greek party they called a symposium where Greeks, but mostly Greek aristocrats, hung out and drank wine until their hearts were content and listened to poetry and music. This was the case in most Greek poleis like Athens, Thebes, Argos, Corinth, etc. but there was one city that was said to be a little different. The polis of Sparta was said by Xenophon that people in Sparta drank wine in moderation for a couple reasons. Xenophon claimed that they drank wine less so they would not embarrass themselves when walking home drunk in front of their paidnomos, the ephors, and the gerousia, the elders of Sparta. Xenophon’s second reason was to improve their ability to navigate territory in nighttime, which made them into better raiding warriors and made their kkrypteia service easier. However, even for these reasons listed by the laconophile Xenophon, it is likely they drank as much as any other Greek when they could for these four reasons. They drank after they competed in Olympic events and other Greek games, they drank when on campaign, they had more Greek festivals that any other polis, and they were a secretive society that did lots of things under the radar.

Spartans likely drank wine at the Olympics and other Greek games because any person who wins generally has some type of non-military victory procession that includes some wine drinking and Greek festivities to celebrate. They do this either in or by the arena where they won or at their home polis when they get back. The Spartans also drank on campaign because not only did they sack places that had wine but they also brought wine via the helots carrying it behind them. Plus, wine was a good drink for campaigns because it was a clean source of hydration (overall it was a lot more watered down in ancient Greece). Third, the Spartans likely drank just as much wine as everyone else because they had more festivals than all the other Greek polis. These festivals dedicated to mythological figures, heroes, and past kings were days where they just drank wine, wrestled, and competed in other sports since they were holy, non-fighting days. Lastly, Spartans were less likely to drink in moderation if they could get away with it because they were a society that was very secretive. They were always trying to steal things without being caught, kill people without being caught, and sleeping with each other in the shadow of the night without being caught. So if there is any credence to how secretive the Spartans were, it was likely they were drinking as much wine as they wanted.

So to answer your question, Sparta was said to be the one society in ancient Greece that said ‘meh’ to wine according to Xenophon and Aristotle but it is likely they drank it when they wanted to. Solely because they are Greeks and the Greeks loved their wine because all Greek poleis could grow a good grapevine and sustain a vineyard. Plus, Sparta was a society that ate together in their commons messes, the sysstina, where people had to bring wine and food to the mess. So it is likely they drank extra wine if it was brought to them by a fellow Spartan. In sum, there wasn't likely a Greek polis that said ‘meh’ to wine because sometimes that was their best drink option and it is the Greek beverage of choice. It was much more likely that moderation was stressed in Spartan messes more than anything.

Some societies, like in pre-Colombian Mesoamerica, had some kinds of alcoholic beverages, but they were only consumed in very particular religious and social contexts, not as an everyday beverage like in the ancient (or Modern) Mediterranean.

I've often wondered about the role of genetics in the development of a society's attitudes towards alcohol, especially since alcohol tolerance and metabolism are now understood to have some genetic component, independent of body mass.