You’re wrong, I think we are arguing different points here.

The concept of “Free speech” exists only because of the government. Without the government, it’s just speech and yes if you are using your speech to be an asshole I would expect the property owner to weigh in.

However, your god given rights as a property owner don’t preclude you from being a statist asshole if you decide to use whatever small amount of power granted to you as/by the property owner to push statist principles and censor dissonance especially when such actions are in direct conflict with an openly stated value of “free speech”.

A much better analogy here is the one posted by OP. Here we have a sub called “free speech” and suppose they flat out banned everyone who participates in this sub (or a specific political ideology). Presumably the mod has that ability granted to them ultimately by the property owner, which makes it ok. That doesn’t mean they aren’t statist shills obviously lacking their own stated values for doing so, and it’s quite a bit different than giving someone the boot for misgendering your guest.