While people who do handle it fine, by that point you've lost a massive crowd that would maybe consider your other advice if not for the "oh, and also you should be vegan" part. The problem of meat production carbon footprint is roughly linear in the amount of meat consumed, so it's enough to tell people to eat as little meat as they can, without asking them to cross the mental/cultural barrier vegetarianism is.

(Also, I'm not sure whether going from vegetarian to vegan means smaller or bigger carbon footprint.)