I'm a lifelong Yankees fan and I don't mean to pour salt on any wounds here, but most Yankee fans hate being lumped together in any way with Red Sox fans. Granted, now that the Red Sox have won 2 world series in recent years, there is a lot more more ammo to support their team...but a lot of the Yankee/Red Sox rivalry was imposed on the entire sports-world by ESPN.
Sure there have been some great teams and games between the 2 over the past decades, but generally, Yankee fans never felt the same way about the Red Sox as Red Sox fans felt about the Yankees. My math may be a little off here, but the Yankees won about 26 world series in the time the Sox won 1. Since the playoffs expanded in the mid 90's (and also when the Yankees became perennial contenders again), Yankee fans usually felt the Indians, Mariners, Rangers, A's, and/or Angels posed a bigger risk than the Sox. But hey, Boston did beat the Yankees in the ALCS several years ago. They've now won 2 titles recently and certainly seem to be a threat to the Yankees every year for the foreseeable future. So now I do consider them a rival. And I'll be honest, I now do take pleasure in seeing the team lose and their fans deal with the meltdown.
To back up ACamp a little, it's primarily been the fans of the Red Sox that have turned me sour on them as a whole. Whether I've been in TX, AR, CA, TN, or anywhere else in the U.S.; obnoxious, fair-weather, instigator fans usually don't do it for me. I remember being at a Monday night football game in Nashville between the Titans and Patriots the year after the Pats won their first super bowl. The Titans dominated the game and knocked the Patriots out of playoff contention. The NE fans at the game walked around like a bunch of billy-bad@sses pretending they were some football dynasty that had finally gotten their chance to sit at the table with the Bears, Packers, Cowboys, and Steelers as historic heavyweights of the NFL. Newsflash-- before 2003...nobody, on any national level, really cared about your franchise! I hate to say it, but basically between 1919 and 2004, nobody outside of New England really cared about the Red Sox either! But hey- both teams are good now and have recent championships to rest on. Good for you guys. But we don't need the fans and ESPN constantly telling us how amazing you are and what incredible, rich traditions your teams have.
