It doesn't have to be advertising; if policies were enacted to either restrict supply (by making it more difficult to produce in favor of some perceived public good) or to raise the price by reducing (currently significant) subsidies or imposing taxes on the supply chain, that might make your fridge less likely to contain those things.

Policy and advertising both work at the margins; if something affects consumer choices such that they swing 10% to or away from a sector, that has a huge impact on the sector. Can you imagine no changes that would convince you to eat 10% more or less meat?

Lobbying is a real thing, propaganda is a real thing, corporate-government collusion is a real thing. The meat and dairy industries are definitely things, and are GIGANTIC, pouring millions and billions into deceiving the public.

If you're looking around the room and don't see the sucker, it might be you.