Here's the thing: I'd argue in the US calling it "feta" is not deceptive, because most people I know have no expectation that feta cheese necessarily comes from some area of Greece.

I have no problem labeling a cheese "feta" if the location of production is clearly indicated. "Feta" is just "shorthand" for "feta-style". Everyone will just call it "feta" anyway. Maybe it doesn't matter if it says "feta-style" or "feta" but the whole thing seems sort of silly to me and a waste of money. It's fighting a losing battle.

It's not that I don't appreciate cheeses from their original locations; it's just that this labeling initiative seems disingenuous to me, in that it seems to be fighting normal processes of language evolution and change.

A better example maybe is cheddar. This is something so entrenched in American vernacular that the idea that we should insist on labeling it "cheddar-style" is clearly unnecessary. When someone says "cheddar" in the US about 99.9% of the time they are referring to a style of cheese, maybe from New York, maybe Vermont, maybe Wisconsin, maybe from England, maybe somewhere else. They're not referring to a location. "Cheddar" and "cheddar" in this context are polysemous homonyms/polysemes.

Arguments about replicating some original flavor of a place of origin are missing the real underlying problem, which is that labeling a product according to its commonly understood meaning, if the location of production is clearly given in the packaging, is not deceptive. Sure, we can tack on "-style" onto everything but it's not going to keep people from ignoring it in speech.