I have had this happen to me many times over the years.
There is another thread on here that asks what people say when another person says to them "Rocky Top" or "Go Big Orange" or something like that. I reply simply "Go Vols!"
When an opponent or someone of another school says something profane or insulting (more often gators or bammers), I simply say the same thing as I said to the person who was giving me a positive greeting, i.e., "Go Vols!" and keep on walking. My thoughts are that the insulting person, for whatever reasons, is very anti-UT so saying something positive like "Go Vols!" is probably insulting and as negative of a response as replying in kind to him as the kind of trash they hurled at me. In fact, I sometimes will hear the person saying another insulting thing as I walk away. From my perspective, hearing that I had annoyed them with "Go Vols!" just makes me smile.