This is a great topic and one I have recently discussed with my wife. I've been asked all of those questions.
I was recently at Taco Casa in Gainesville when a teenage guy working there came up and asked me if I worked for Valley View. It dawned on me that I was weaing my mesh coaching type cap that only has the Eagle on it and is green with a black bill. I told him know that it was a Mean Green cap. All of the coaching/working for UNT then started up. Living north of Denton I get alot of Valley View comments when wearing Mean Green apparel. Valley View is about 20 miles north of Denton, near Sanger, and they they are the Eagles and their primary color is Green. I have about 20 UNT shirts/jerseys and about 10 caps, so I regularly have something on. I have a dark green #81 jersey that I frequently wear. When T.O. played for Philly I used to always get, "Why are you wearing that? I thought you didn't like him and were a Cowboys fan."
I get the Aggie ring question as well. That one doesn't bug me as much, because my wife got here undergraduate degree there and I went to grad school and worked for them for two years. I usually just respond with "No, it's my North Texas ring, but I did go to grad school there." I understand the confusion with that one.
Having recently been traveling for work and vacation and wearing UNT gear I had three different people in three different locations come up and say something about UNT, Denton, or the Mean Green. All was positive. I have found that to be a common occurrence when traveling.
Hang in their guys. Keep wearing your UNT clothing, caps, rings, etc. UNT needs to push their way onto the scene, much like Texas Tech has the last decade. I remember when Tech pretty much stunk and UNT stuck it to them several times. The number of current UNT students and alum is tremendous, but people need to be more outspoken about their school. I'm pretty much sick of the "I went to UNT, but I'm really a __________ (insert team-usually Longhorns) fan."
One thing I have done every Super Bowl Sunday for the last ten years or so is that I have an annual family/friends football game. It took a little time time and money, but my team (which usually consists of about 7 or 8 guys) wears a Mean Green jersey. No other teams allowed for my side. It is nice to take the big photo at the end and have all the tech, horns, sooners, etc. fans standing there in Mean Green gear. Those pics are framed and set in my office at home and work each year. Go Mean Green!