The Red Sox Chick is great, but she's taking the Yankees too seriously. The fans pay a lot to go to Yankee Stadium and they are getting their money's worth. They boo or cheer depending on the game and how they feel, and then go home and don't think twice about it.
I've lived in both Boston and NY, and the Boston fans pay way more attention to the Yankees than the Yankee fans do to the Red Sox. The only real time Yankee fans pay any attention to the Red Sox is when they are playing, or at the end of the year if the race is close. Otherwise Yankee fans don't care about the Red Sox. But the Red Sox fans are obsessed with the Yankees all the time.
The atmosphere is completely different at the two parks. The Red Sox fans are at Fenway for the game. The Yankee fans are at Yankee Stadium to be entertained. That's why the Yankee fans seem crazier with boos and cheers. They don't just want to watch the game, they want to be in it.