Okay lets get this straight, animals do not contribute to global warming. The co2 they emit has been taken from the atmosphere from plants.

Methane breaks down to Co2 in the atmosphere on average in 9.6 years.

Animal rearing does not permanently affect the climate.

Increasing stock sizes does increase the methane level equilibrium but there are mitigations to this, there are additives to feed that can reduce methane emissions to 1%. Last I checked a few years ago, there were pilot programs to determine effects on animal welfare and product quality.

The problem we should be focusing on is fossil fuels.