That just doesn't make any sense to me. People can be offended about anything, and you have no control over it. However, you do have control over your usage of a word and how you're using specific terms in language, so doesn't your conception of how you're using the word ultimately determine the moral nature and appropriateness of your words/language?
I suppose in theory people can be offended by anything. If you respect other people enough to assume that they usually have a reason for being upset about something you do, it might make sense to at least give other people the opportunity to explain why what you did upset them.
You do, after all, have control over your own actions and word choice, and while you aren't necessarily obligated to do so, making an effort not to do or say things you know will hurt the feelings of those around you seems to me like a fairly basic part of being a decent person.
I don't know about "moral nature," but I do know that your own conception of what you meant doesn't have anything to do with whether it bothers or even deeply upsets somebody else. Now, sometimes that's going to happen because of a misunderstanding on their part. Sometimes it's going to happen because the other person is extremely emotionally fragile. But other times it's going to happen because of your own ignorance.
In any case, why not try to at least understand where the other person is coming from? And then, if it's not a hardship, why not try to avoid upsetting them in the same way in the future?
Liberal / Western conceptions of free speech and moral autonomy ... well, I don't know. But it seems to me being part of a diverse society asks something of you to give a dang about how your actions affect other people. Right? Doesn't mean you necessarily have to change your behavior. But it should factor in.