Bonnie, I can't say if vinegar in the water deters mosquitos, but I can tell you that I haven't seen mosquito larvae squiggling around in the water before changing it out, either!
Quite possibly because I do change out the water at least every other day, or more, if possible. I don't ever leave standing water in the bath for more than 3 days TOPS, though.
Vinegar in the water simply buys a day or two for busy gardeners to change out the birdbath water when time allows, and it makes for a quick and easy cleaning. ....and, yep....environmentally friendly and, best of all, it's cheap!!
I certainly do not recommend leaving standing water with vinegar in the birdbath for days on end, whatsoever!!
It's not healthy for the animals, and I would venture to guess that mosquitos may be just as likely to breed in a *neglected* birdbath with vinegar in the water, as they would without vinegar in there
but I'm a simple home gardener, not an Entemologist!!