There is a prescriptive school of thought according to which things like John and me are hungry ought not be used. It is based on the logic that me is for objects and in that sentence one ought to use the subject form of the pronoun, which is (of course) I.
That logic is perfectly valid (and for whatever it’s worth, I myself almost always do form compounds according to the logic). But its validity doesn’t guarantee its “legal force.” Consider, for instance, that French civilization isn’t utterly collapsed despite the fact that their analogous construct, *Jean et je, would never ever be accepted. French permits only Jean et moi, even as the subject of a verb: Jean et moi, nous avons faim. Now sure, French isn’t English; I give this example merely to illustrate that strict, formal logic is not an absolute requirement for any natural language.
Using things like John and me regardless of syntactic context has a very long pedigree and very widespread use.
So whether to use it depends on context. If in a formal register, then selecting one’s pronouns to accord with their syntactic surroundings is advisable. But in more laid-back contexts, the so-called prohibition of John and me are… can be taken with a grain of salt.