Under conditions where animals self-feed from their environment and there's enough of their food source, meat will be available, but just much less often than today. Cows produce milk mostly after they've been pregnant, so there will be calf production, usually above the carrying capacity of the environment. This "excess" would create an incentive to kill cows every so often for meat, but we're talking on the level of one per year or less. Or for chickens, maybe one per month. This is fairly consistent with how often humans with livestock have usually had meat, which is as a special occasion kind of thing. If you kill a goat twice a year for economic reasons, do so on a special day.

So it's interesting to find vegetarian societies, as it means they didn't have livestock or they made a philosophical choice to not eat the dead ones.