In short, I don't think I buy your claim that "Some empirical statements, orthogonal to truth or falsity, are offensive." At least, I'd like to see it supported better before I consider it.

Some examples of empirical statements with questionable-to-bad ethical undertones. I present them to you as food for thought, not as some sort of knock-down argument.

• "Your husband's corpse is currently in an advanced stage of decomposition. His personality has been completely annihilated. Remember how he sobbed on his deathbed about how afraid he was to die?" (Reminding a person of a bad thing they don't want to think about.)
• "Ladies and gentlemen of the jury, here are twenty police case files on convicted child murderers, all of them Albanian just like the defendant, without any statistical context." (Facts presented in a tendentious manner.)
• "Just thought it might be interesting for you to know that women tend to do about 10% worse on this test than men. Anyway, you may turn your papers over now - good luck!" (Self-fulfilling prophesies.)
• "You're the only asian in our office." "Did you notice how you're the only asian in our office?" "Maybe you didn't realize you're the only asian in our office." (Drawing attention to & thereby amplifying the salience of an ingroup/outgroup distinction.)
• "All I'm saying is that girls who wear revealing clothing are singling themselves out for attention from predators!" (Placing blame for a moral harm on a blameless causal link leading to the harm.)
• "If he dresses effeminately like that, he's going to get bullied." (Ditto; also, status quo bias.)
• "A black man will never hold the highest office in this country." (Self-fulfilling prophesy; failure to acknowledge shittiness of (purported) empirical situation.)

I think that the ability and right to say true things regardless of whether someone finds those truths unpleasant is extremely important, and social norms to the contrary should not be adopted or perpetuated lightly.

Not lightly, no. But as I was saying to Daniel_Burfoot above, there is just no avoiding the fact that statements, including statements of truth, are speech-acts. They will affect interlocutors' probability distributions AND their various non-propositional states (emotions, values, mood, self-worth, goals, social comfort level, future actions, sexual confidence, prejudices). Inconvenient as human mind-design is, it's really hard to suppress that aspect of it.

But there is a big asymmetry here - you (the speaker) know what you mean, so if it really needs to be said, take an extra second to formulate it in the way that has the least perlocutionary disutility.