I don't drink either, and never have done. My husband does though, although he doesn't drink wine, only lager.
When we got married, we took advice on what wine to provide with dinner because as neither of us drink it, it would have been pointless trying to choose a nice one - we both think they're all foul! (And I made a big effort to ensure a nice range of soft drinks was provided - all this fuss for drinkers to have something nice, and as a non-drinker you are so often stuck with coke or orange or similar - again. Bleugh. I like drinking nice things too, so for our wedding I bought elderflower cordial, and a couple of varieties of sparkling grape juices and the like.)
When we go out, I tend to pay for drinks separately. I know people say that soft drinks are almost as expensive, it's true, they are. But, I also know that when most people go out for a nice meal they drink more in terms of quantity than I do - I have a glass of orange or coke to quench thirst, whereas in my experience most people going out for a meal drink more than they normally would because it is part of the social experience for them. So I do object to subsidising a £25 bottle of wine, when I've had an orange at £2.00. But it's never caused a problem - I've never been in a situation where people get that worked up about it. If I've drunk more than that, or they've drunk less, or I've had a pudding and they've not, then we might split evenly. I really don't have a set-in-stone rule for these occasions! (I talk to my friends and we make a decision when it's time to pay the bill!).
In terms of people coming to our house, we don't buy wine. Again, we'd have no idea what to buy, and I don't really want to offer up vingegar. My DH will get some beer, and I buy in some really nice soft drinks. But most people who know us know this and bring wine if they want to drink it. Again, it just doesn't seem to be an issue. But then my group of friends are an informal lot and this sort of thing has never been a big deal. Same as, if I go to someone's house, I buy myself a really nice soft drink to take, because most people have coke or squash or water, and to go with a nice meal, those are not appealing options.
None of my mates seem to hold any of this against me - we've been friends for a decade or two - so clearly the wit, companiability and geniality of the dinners we have outweigh the lack of wine!!! 