A carbon tax would do so. Unfortunately it's hard to get anything done nationally, much less globally
In lieu of that, despite variance in environmental impact across foods, on the whole, the average vegan diet is almost certainly going to be far better for the environment than a non-vegan diet.
And this is not even getting into other positive elements such as health and animal welfare, but those are unrelated topics likely to spark additional argument, so I won't go further.
Emissions are not a significant consideration in this global economy. The key factor that everyone cares about is cost.
https://www.colorado.edu/ecenter/2022/03/15/it-may-be-uncomf...
Climate change is primary caused by humans burning fossil fuels, and humans extracting fossil fuels to be used in chemical processes like artificial fertilizers. In the short term it might be beneficial to reduce the number of animals that eat plants that has sequestrate carbon from the air, but in every case it would be worse if we humans use fossil fuel to burn the same plants.
Some people has argued that in the very short term, reducing methane while increasing emissions of fossil fuel emissions could beneficial be a better strategy if we can know for sure that carbon capture will save us in the future. I am doubtful to that strategy.
It should be noted that methane leaks from fossil fuel industry is larger than that from cows. A primary source of those methane leaks are the production of artificial fertilizers, but of course all steps between extracting natural gas to producing the fertilizers has large amount of emissions and leaks.
Solving that faster, is what is needed. Maybe instead of having everything be handled at the top level inter community personal outreach is needed.
What you eat is personal - having an impact on emissions/environment is not solved at a personal level, it requires nation level negotiations.
What you eat is at best a signal to higher level political groups of your inclinations.
Political groups are lazy and/or inept and will assume such.
As far as veganism is concerned, it is notable that it is much easier to be vegan now than 20 or even 10 years ago, as vegan ingredients are more widespread and higher quality, and "vegan options" are essentially standard in restaurants. This didn't happen through legislation, but by the application of social pressure by vegans - if vegans can't eat at your restaurant, they won't just go somewhere else, they'll take their friends with them. It is the output of a massive multiparty negotiation.
The top thing is for people to consider emissions and allow emissions to become part of the decision process. In terms of diet that could be to introduce and consider food outside of the cultural limits, like shell fish and sea weed. A related issue are that a large number (majority?) of Europe and northern American lakes has major issues with eutrophication with mostly fish that people refuse to eat because of culture. Eating those kind of fish would solve two problems at the same time, feeding people and removing uncontrolled overgrowth caused by artificial fertilizers.
Right now it is also cheaper to operate heavy machinery that run on fossil fuels to control plant growth in nature reservation and around power lines, rather than raising animals that would do the same job and create food. Same thing with Lawn mowers. One of the most ecological method to keep grass cut is (real) free range hobby scale chickens. Produce food, cuts grass and keeps pests away.
As with everything else, everything change if people allow emissions to be part of the decision process.