It's complicated. Some places in the world, livestock is grown quite sustainably and are basically neutral climate-wise. Other places, it is an unmitigated ecological disaster (clearing rain forest, for example). Because we produce so much around the world, on average, it is pretty bad.

Generally, livestock takes more land than grain crops in order to produce the same calories. However, there is more to nutrition than simple calories, so optimising for calories per hectare is probably not the right answer either. I once saw a report suggesting that you can feed more people with less total impact if you include livestock in the mix because livestock can graze on more marginal land than you can farm crops on. I am not qualified to comment on the veracity of that report.

I think, in the end, going vegan for climate change reasons is an extreme and unjustified position. On the other hand, almost everyone can stand to eat less meat than they currently do and would probably be healthier for it (myself, included). If we reduce overall meat consumption, it would definitely be a net win for climate and ecology reasons as we could concentrate on producing more sustainably on average than we currently do.

Sheep, like cows, are ruminants and ruminants burp methane, which is a greenhouse gas. Per unit of lamb or beef, about two-three times[1] as much of greenhouse units ("CO₂ - equivalents") is produced than for pork. Chicken has an even lower carbon footprint.

I think it is evident that many in the Western world eat more meat than they need to to stay healthy. The best for your health and the environment is probably to eat an as varied diet as possible, with lots of vegetables to complement your meat/protein intake.

[1] numbers differ depending on who you ask, and on which farms were measured.

Going vegan is one end of a spectrum.

You might also change your meat choice. Chicken is far better than pork, which is far better than beef. No need to instantly go cold turkey on meat if it doesn't suit you.

Production of animals for meat and dairy at large scale using crops grown with fossil fuel inputs is bad for climate change, not traditional grazing.

Traditional grazing doesn't achieve the scale of industrial agriculture though, so the products are more expensive.

You don't have to "go vegan" but reducing animal product consumption in general is an accessible way to minimize your climate change impact.

Wool > Polyester.

Shade is good for a sheep. Not getting eaten is even better for a sheep.

Raising millions if not billions of sheep, that's bad for the environment.

But you knew this already...