The better question is whether or not meat can be produced sustainably. Humans have been raising livestock for millennia, and climate change only seemed to start after the Industrial Revolution, so meat isn’t obviously necessarily causative of climate change.

To my understanding, the climate problem is basically one of not having closed loops. For instance, burning fossil fuels is a problem because you’re taking carbon that’s buried underground and pumping it into the atmosphere. So to the degree that meat is a problem, there’s probably a loop we need to close. Energy and transportation are instances of the same burning-fossil-fuels problem that we need to solve anyway.

As for the livestock themselves, I know they produce methane as a byproduct of digestion, but that seems like a potentially closed loop to me. Wasn’t it a closed loop during all the centuries that humans raised livestock before the Industrial Revolution? If so, what changed? The way we produce fertilizer, for one. But we also need fertilizer to grow vegetables, so we need to solve the fertilizer problem anyway. Plus, livestock are also the primary source of organic fertilizer, so maybe they’re part of the closed loop. They sure used to be.