Effectively if you would stop commuting with a car, reduced AC/Heating to bare minimum and simply bought less 'stuff' (non-essential goods), you would be doing more for the environment than not eating meat.
The unconfortable truth is that once we start discussing these things very few people are willing to curb their 'standard of living', in reality it is a first world luxury not a given right.
Nevertheless if you tell me that we need to curb meat consumption to avoid animal suffering than I am equally on board with you. But the environmental angle in my view is a distraction from the other elephants in the room.
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.