I've booed one player at a baseball game, and it was John Rocker. For being an all-around terrible person. That's the only time it was ever justified. Sure, paying ticket holders have a "right" to boo, but that doesn't make it any more sensical. It's completely idiotic to boo someone who is trying as hard as they can to be the best player they can be. There is no proof that he's done otherwise.
Also, I have a question. What would the Twins have done with the money saved by not paying Mauer? Signed one ace to a bloated contract? Signed a couple average pitchers? Maybe a couple average position players? Either way the Twins would still be terrible. The problem is the farm system. You can't build your team through free agency unless you're the Yankees, and even they are good at developing their own players. So if you want to boo anyone, boo the front office, the scouts, whatever. If that makes you feel better.