I guess you can put it on display in your home, but it's especially weird if you are wearing a championship ring, for a team which you had no part of, out in public. You may think it's perfectly normal, but I think most people would agree with me. In fact, most players who earn championship rings keep them in a random box in a desk at home, and some of them end up selling them if they are in need of cash.
If you are wearing it out in public, you are doing it to draw attention to yourself. So, when someone asks you "hey man, cool ring, were you on the '95 team?" you have 2 choices. You can be honest, which draws questions of "why do you have that ring then?", or you can lie, which makes you look like a bigger d-bag.