I don't drink alcohol, and I also belong to one of the religions where alcohol is explicitly and strongly forbidden. As such, I avoid, as much as possible, where alcohol is served, which is challenging at times, but I make do.
However, I never asked someone not to drink on account of me (though I've definitely given advice to avoid it to people as I would advise anyone to avoid something that is harmful, which I believe alcohol generally to be). My way of dealing with this is to avoid places expressly for the purpose of drinking alcohol (e.g., bars) and to avoid, as much as possible, being the presence of it when it's being drunk.
But those are actions I impose on myself, and not others. I fail to see how this is conflicting with the accepted ideals of liberal democracy (which you ascribe to my entire faith, apparently) and how that is a judgment on people, or how what I do or believe concludes that people are unclean/mad/whatever.
Having said all of that, if the accommodation were made to offer an alcohol-free alternative to something that otherwise is not, I would overwhelmingly welcome that, as I imagine anyone in the world would overwhelmingly welcome any accommodation to their own choice in beliefs, practices, limitations, or other factors that everyone has to some degree, as long as it were not cause to exclude anyone.
One of the differences here is that, by choice, I cannot drink and prefer not to be around alcohol, but I fail to see how a lack of alcohol is an equally discriminating thing. I would argue keeping alcohol out, while maybe less enjoyable for some, would make the environment overall better for most due to the lack of people getting drunk and doing things they otherwise would not do, cost would be significantly reduced, and once again, allowing more people to attend than could otherwise due to the reasons outlined throughout this conversation.