Sorry, but I am too tired to read all these posts, so this has probably been said already.
I have a Hiatus Hernia, fruit based drinks (including wines), and any fizzy drinks, give me awful heartburn, and I am already on two prescribed Omeprazoles, and up to eight Gaviscons a day. Water, weak tea, milk, and curiously tomato juice, are the only drinks that I have discoved so far, that don't give me painful reflux. I do find it strange that I can eat most fruits without a problem - the fruit's flesh must somehow make a difference, maybe it is just because chewing produces mouth acids that help to neutralise the acid/alkaline's affect on my body.
Anyway, in a proper restaurant, rather than a fast food one, I would drink water, but it can be boring to just have water all of the time, so in a fast food restaurant I will often have milk as my drink instead (I can't stomach milkshakes either, they give me acid reflux too), and having been through the menopause I like to think that the milk might help my calcium levels as well!
The gentleman on the OP's date might have a similar problem to mine, and maybe he hates water, or maybe he has enough self-confidence that If he fancies a glass of milk, that is what he will have. If it is the latter I think I would actually find his self-confidence sexy, as long as he wasn't arrogant as well, as I hate all arrogant people! If he, like me, had digestive problems then I would of course think it was fine as well. In another scenario, if I knew he was on the spectrum, but he was someone that I found attractive and interesting, then I would again have no problem with him drinking milk.
In fact I am not sure why a date drinking milk should be a problem at all? I suppose it would just seem strange to me if a blind date ordered a glass of milk, but why - except maybe because I am the only adult that I have ever known, to order a glass of milk whilst eating out - it would seem strange, I just don't know. I think that I would have to try and ask him as tactfully as possible, why he wanted to drink milk with his meal. Of course, that could easily backfire on me, if I was happy with his response, but he wasn't happy with me asking him in the first place!