IMHO, the workable solution is to get people to eat vegetarian once in a while, eat less meat in general (which is even good for one's health, as at least in the West people eat way more meat per-day than recommended) and turn eating beef (and, to a lesser extent, pork) into something that is more unusual than usual.

Reduction and more climate-friendly meat consumption is way easier to sell as an idea to beings who are omnivore (so have a natural desire for the stuff) than full vegetarianism (or, worse, full veganism) and I'm pretty sure some of those people will end up mainly or even totally vegetarian and even vegan, as they get used to and appreciate meat-free meals.

However the Moralists are as usually abusing and distorting a genuine concern to push an absolutist view (as it's anchored above all on a Moral viewpoint on meat consumption, so Environmentalist objectives are at best secondary), damaging the actual Environmentalist outcomes since it's a lot easier to both convince people to slowly rebalance their meat-consumption and have it happen in a safe way for even the less informed than it is to do it with sudden total abstinence.

I mean, if we're looking at the graphs, beef really is the only "offender" (if you can call it that) and only in the current consumed amounts. If people ate a lot more chicken and less beef, the GHG effect from animals would be lower than the same number 500 years ago due to animal population culling and advancements in agricultural methane reduction.

At that point, the term "negligible effect" becomes unreasonably harsh. Even with the worst claims against the effect of livestock on the environment (many of which we might not see eye to eye on), it's simply objectively not an environmental issue if people are eating chicken and some pork as their staple proteins. You can call it an animal rights issue if you want. Considering chicken is almost objectively a correct and healthy food to eat, two thirds of the diet triforce (health, environment, animal rights) become non-issues.

And the cool thing, even if I disagree with the outcomes it's healthier for us to eat a bit less red meat as long as our meat protein intake stays reasonable from white meat and seafood.