The reason why the idiot libertarian argument doesn’t work re segregated restaurants in the South is because it ignores reality: had another restaurant or diner opened nearby the segregated one, and served blacks and whites equally, it would have been bombed or set on fire. Plus whites wouldn’t have patronized it. It is a historical fact that the racist negro-phobia was what controlled the social order then - whites who ignored or flouted it put their own lives at risk.
The oppressed black thing has no application to the gays as bullies situation. The fact is that homosexuals are the dominant force in all the aesthetic businesses - fashion, design, decor, event planning, food service, etc. You’d have to look hard to find a non-homosexual vendor of these services - unless you are way deep in a rural area.
You also missed another point. The (Democrat controlled) government passed laws that said restaurants had to be segregated.