How to get out of an uncomfortable egg culture situation with this one simple trick.
Real talk: Calling people eggs is a violation of the egg prime directive, and is considered invalidating as you are trying to say that a person is not the gender they identify as, that their identity is invalid. Don't call people eggs, like ever, it's extremely uncool.
I think there's enough difference in the context and tone that these two use-cases don't really collide much besides being the same word.
"Egg" on its own is generic enough that it really needs context to know what one means, usually said context is situational.