> going vegetarian reduce one's environmental impact

Mmm, yes and no.

It depends where your meat comes from. If you buy meat the way it's produced in the US where you have great big sheds full of cattle in the desert with everything trucked in, then yes.

If you want permaculture, you absolutely must have livestock.

If you want arable farming of any sort, you absolutely must have livestock.

The whole thing breaks down very quickly if you don't have grass and clovers growing in fields, and ruminants eating them, breaking down the tough cellulose, and then shitting it out and trampling it in.