The short answer is that everyone is different and will respond differently to any sort of public interaction. It's normal for them, even if it seems weird to you.
Having lived most of my life outside of Tennessee, and having traveled all over the world, I have had a lot of these interactions.
1. Ignored. Didn't hear me, didn't understand me or just didn't process what was happening. There are a lot of busy and distracted people out there.
2. It's just a shirt. Sometimes it was given to them as a gift and sometimes they don't even remember where they got it. Maybe they picked it up for a dollar at Goodwill. It has no real significance to them, other than it keeps them covered up when they go somewhere. "Huh?" and/or a puzzled look usually follow.
3. They're fans, but they're just not familiar with the etiquette. Some Vol fans have never been to a game or spent time around other large groups of VFLs. So when they are suddenly in an unfamiliar verbal exchange, they are stumped for how they should reply.
As for me, it depends on the situation. But there's always a "Go Vols" in there somewhere. Sometimes it is preceded by a "Yeah, baby..." and a fist pump -- or even a high five. If I am surprised by the salute, I will usually say something like, "Alright! Yeah, Go Vols." When I see them first, I have been known to start-off with, "Hey, I like that shirt/hat/golf bag," followed by a "Go Vols."
No matter what, though, I always enjoy seeing our brand represented wherever I go.