If the price for alternatives goes down in return, sure. Tax meat more heavily, subsidize vegetables and plant-based alternatives with that tax, or come up with some other clever scheme. It'll drive change a lot faster than just depending on the few who (can) care enough.
We eat, on average, too much meat as it is, and with meat the negative externalities such as deforestation are completely ignored in the price.
Subsidizing a bad thing so more people can do it doesn't make it a good thing. I also eat meat, but the main argument here is "let's have meat prices more accurately reflect the cost and let the market adjust accordingly", and then as a bonus it should also help the planet and everyone
I don't know about medieval times, but a lack of animal products in the diet of the the impoverished and imprisoned was a problem as recently as the early 1900s. The disease Pellagra[1] is caused by a lack of niacin in the diet, which can be commonly found in animal products (and certain plant products like legumes). It was considered a paupers disease and was most commonly found in rural areas and in the poor, imprisoned, or orphaned. The prevailing theory was that it was related to eating corn - either an insect born illness or a contaminant - when in reality it was a lack of diet diversity in the people who could only afford to eat corn. The history on Dr. Goldberger is actually really interesting and I recommend a skim of his Wikipedia page.
It depended on the climate and society. Pastoralists living on the steppes almost exclusively lived off animal meat and dairy products, while folks in areas with heavy grain production were much more likely to get the vast majority of their calories from staple grain crops.
