I don’t think most people will have a problem switching to plant based burgers as long as they taste good, but I think that’s still the sticking point at the moment. I’ve had an Impossible burger a few times and could always taste a strong difference (I even did a few blind taste tests). I don’t think it’s close to actual meat yet. Supposedly the second version of the burger has improved; I haven’t tried it yet.
Cheap meat, like ground beef, will be replaced first, but I think it will be much more difficult to replace specialty meats: Iberian ham or Wagyu for instance. Good luck making something plant-based that tastes like that (not saying it can’t be done though).