Making food prohibitively expensive is not cool. Leave what other people eat alone. >:-|
I empathize with the position that any tax on a food item will disproportionally impact the poor. And I agree, everyone should have a baseline level of housing and food accessible to them regardless of their circumstances. But if a food item has huge negative externalities, surely we should do something to limit its appeal and consumption, right?
Anecdotally my own experience switching to a diet with less meat is that food costs have gone down.
Cheap meat available to the masses isn't going away. Pandora's Box has been opened, we have to deal with that. The only thing accomplished with making meat prohibitively expensive is pissing meat-eaters off (thus them resenting any environmental reforms even more), and most importantly, making it accessible only to the wealthy.
It's fine to offer healthier alternatives, but don't expect to be moving mountains. Focus more money and effort on lab-grown meat.
There are still health concerns around a diet heavy in red meats, but at least it would address the environmental issue.