https://www.epa.gov/ghgemissions/sources-greenhouse-gas-emis...
It's not the largest contributor, for sure. But it's sizable.
https://www.nature.com/articles/s41598-017-06466-8
Reducing meat intake _does_ sizably reduce overall emissions.
Honestly the links between diet and health are always thin at best, but I don't know of any that strongly link a well-balanced vegan diet with reduced health. Usually, the opposite.
https://academic.oup.com/ajcn/article/89/5/1627S/4596952
> "In general, vegetarians typically enjoy a lower risk of cardiovascular disease (CVD), obesity, type 2 diabetes, and some cancers [...]"