Mass starvation probably. We aren't prepared for it. Give it 10 years and maybe it could be done.
> would it actually cut down emissions, methane? co2?
You'd have to do something about all the existing livestock. Again with 10 years' lead time you could just stop breeding new livestock and let them die out.
> but [what] would be the impact long term
Less deforestation, less fertilizer (and therefore fossil fuels) used, lower methane emissions. If people could adjust their diets the impact would only be good (other than losing meat and dairy, which would be sad).