(You won't be surprised to learn that I've written about this before, but it's something I'm frequently confronted with).
Pet peeve: "It's only censorship if it's the government censoring you."
The government does not have a monopoly on censorship. The fact that the right to freedom of speech is written into our code of law means that we have recourse to the law only if it's the government censoring us. That does not mean that the law supercedes any other interpretation of the philosophical concept of free speech and censorship. If an art gallery, business establishment, individual, or internet service silences you, that is still censorship. It's just censorship that is permitted by the law.
Do private entities have the right to construct intentional environments around themselves? Yes. Should they? I think so, yes. But should they also be held to the principle that an atmosphere of free speech is a generally desirable thing? That is my belief. There are cases where what could be construed as "private censorship" might be justified (e.g., to create non-threatening spaces for vulnerable populations). But in any case, the action of restricting citizens' [local, if not universal] freedom of speech should be taken reluctantly, within considered limitations, and only with good reason.
Because the idea that "if you can't say something here, you can just say it over there" - which is used to justify private censorship as opposed to government censorship - holds increasingly less water with the more places that crop up where you can't say that particular thing.
Also: I make a distinction between censorship and harassment. If you use your speech as a weapon to harass somebody, you should be silenced (and ideally removed from the situation). This does not mean your ideas are being censored, just the way you're using them (i.e., you're being punished for being a jerk, not simply for saying whatever it is you said). Find a way to express your thoughts that isn't directed toward a specific person in a hostile manner. Freedom of speech is not incompatible with human decency (and behaving like it is gives its detractors more fuel for criticism - so let's not encourage this odious idea).