I could see beef dropping a bit. Cattle do suck up a lot of resources, and if feed progresses on a tight cycle, beef prices will force some people to eat less of it. Which could have an effect on future herds.
Dairy could see a downturn- I know that isn't really meat, but if cattle start going down, I wouldn't be shocked if cows started going down too.
Pigs would kind of worry me- they eat a lot of feed too and if feed isn't available I wouldn't be shocked to see farmers return to practices that promote Tric. So pork might not drop as much, but it could return to the days of cook it till it's practically useless.
I'm not sure how much sheep would be affected, but they are a multiuse animal, so I'm betting we will hang on to them harder.
I don't think goat would be too affected, they eat anything.
I think poultry will just keep on as it has been- and may even see an increase.
I think fish farming could be hard hit, especially tank farming. Of course wild farming could be increased. Wild harvesting could get out of hand.
Game- wow, there's a lot to be said about game. It could see a resurgence on the dinner table- or it could be that farmers really strike them down in attempts to save their domestic stock.
Domestic pets and other animals of the "OMG you can't eat that" kinds. These may see an upsurge. If people are that starving for meat, they might start to question it less what meat it is.
And of course there is always large rodents- rats.
I do have to wonder though... If things got so bad that we had to start producing less meat sources, wouldn't that affect some plant sources as well? Or at the least, the way we use water for those plants? Why yes, it probably would.
Perhaps it would behoove us to not panic about water just yet. Perhaps we should start concentrating more on what we have. Food waste is an abomination, distribution sucks, and a lot people are flat out ignorant about food from a nutrition standpoint. I'm sure those subjects are probably rants for other threads though.