I think it's important to note here that whether は or を is used, the お酒is always the object of the sentence.
You must have heard already that は is the topic marker, が is the subject marker, and を is object marker. That's right, は denotes the topic of discussion, which may NOT necessarily be the subject.
Consider the following examples:
私は食べます。 (literally) As for me, eat.
Here, we first bring up 私, and mark it with は, this is the topic of our discussion. Thus instead of "I eat", a more fitting translation is "As for me, eat." It just happens that 私 is also the subject.
お酒は飲みません。 (literally) As for wine, I(or someone else) do not drink.
Here, the logic with the は does not change. We first bring up お酒 as the topic, then, as for the お酒, I or you or some other guy does not drink it. The true subject who's doing the drinking is not mentioned in the sentence, and is implied to be the speaker. If you do wanna mention it clearly, you could say お酒は私が飲みません。
Such is the logic of Japanese sentences, the idea of a "topic" doesn't really exist in English, and the best approximation you can do it translate XXは as "As for XX". Which could be the subject, the object, or neither, just a piece of information that we're setting as the topic, like the following sentence:
公園には私が行きたくない As for to the park, I don't want to go.
Subject: 私, object: none since verb is "to go", topic: directional adverb "to the park"