I don't say this to be offensive, but I say it because you asked the question.
Please don't call me a jealous in response and please don't resort to flaming the Jazz and Hawks.
The answer is yes. Not only are you the most hated team in the country, you are BY FAR the most hated team in the country. I actively root against you. Everyone I know who follows the NBA actively roots against you. I'll often hear the question- who do you want in the finals. The inevitable answer is always two teams followed by, "really, anyone but the Spurs."
We're not jealous. It has nothing to do with your rings other than the fact that people don't like you or your players to begin with and the fact you win championships makes it that much worse. You are just not a likable team. Bill Simmons had a podcast this week where him and Matt Berry were speculating as to why people dislike Kobe so much. Berry basically said that for whatever reason there are just people you look at and right off the bat you either like them, or don't like them. Kobe is a just a guy you don't like. The same goes for your team. Duncan is not likable. His personality and his game bore people. Ginobili is downright hatable- His flopping and unconventional play really gets under opposition skin. Parker is not likable. The way you play is very, very effective, but frankly it isn't very likable. There are very few athletic highlight in Spurs games you know. You just go out and quietly kill people- which is not likable. Your arena and court design are not likable. Your crying about fouls all the time is not likable. Texas as a whole, is not very likable. Basically, people look at you and just don't like you. It sucks for you, but based on the mundane product on the floor, the effecicacy of said product and the often en led at ude of the team, it shouldn't be very surprising.
I used to root big time for the 90's Jazz teams. Everyone hated us. It's not because they were jealous. In that case they would have hated Chicago. It's because we were a slow, effective, flopping & hard-nosed team from a small, rural market and we had unlikable players. It was effective and beautiful basketball, just like the Spurs of today, but I understand why they hated us. In other words- I don't get why you guys don't understand the same thing about your team?