I think it depends on which type of BYOB it is.
If the emphasis is on "Your" (ie, you bring what you personally want to drink), then it would be rude to not bring alcohol but expect to drink what other people had brought (swapping drinks is different). If you didn't drink alcohol, then you could bring a non alcoholic drink instead. Deciding to go in on something with friends is an option - say, sharing a six pack or a bottle of wine by pre-arrangement.
If it's a BYO to share - ie, the alcohol contributions are pooled, and people are free to help themselves - then bringing some nice mixers and garnishes would probably be appreciated, if the alcohol choices tend towards hard alcohol. Or, you could bring a six pack of some interesting soda as a contribution.
If you don't eat meat, you could bring a veggie burger, or just go with the sides.
In my experience, BYOB tends to be done primarily for economic reasons, with a younger crowd, as otherwise hosting a party could be prohibitively expensive, particularly considering that many of your guests will not be in a position to reciprocate. BYOM is sometimes done for economic reasons, but often because the hosts don't want the headache of having to provide half a dozen different options in unknown quantities to satisfy everyone's dietary peculiarities.
It sounds like this case is the second for the meat - the hosts are providing it, but if people don't like what's offered, it's up to them to bring their own alternatives.