I guess you mean “a person who follows an ordinary diet” - a “meat eater” is another name for a carnivorous animal.
They don't “have to” but if I invited a vegetarian to my home for a meal it would be rather rude and insulting to serve them meat. Why would I want to do that? In the same way, if I knew someone was allergic to peanuts or shell fish then I wouldn't serve them those things. We have a friend who I know dislikes lamb. If she’s coming for a meal we don't serve lamb. We don't “have” to do this but we choose to.
If I'm invited to a vegetarian's home then I expect to be fed vegetarian dishes because that's what they eat. If I went to the home of someone allergic to nuts then I would be very surprised fo be served anything with nuts in it. If I dined with, say, people originally from India or China - people who had retained some of their culture - I wouldn't expect, or want, roast beef and Yorkshire pudding or a burger.
I don't think that a French person who loved snails and frogs' legs would expect to be served them in an English home where these things aren't even considered “food” by most people.
As a non-vegetarian, I have no problem with vegetarian food - most of what I eat is vegetarian. I'd expect a vegetarian WOULD have trouble with non-vegetarian food though.