I am not a baseball fan or follower, but this Y/RS rivalry is so pervasive that is gets into EVERYTHING! It is nearly impossible not to get swept into it in your daily travels.
I was at a very lovely wedding last weekend: The Groom a Yankees fan
The Bride (and family) a Red Sox fan
The matron of honor--sister of the bride toasted the newly-weds and roasted the groom in the process by pointing out that although he was a "Yankees fan" (which drew loud boos from the crowd!) and her sister a "Sox fan" (loud cheers) that if the greatest rivalry in baseball couldn't keep them apart, then they were obviously made for each other!
Since I have no particular concern or fan loyalty, I can pick the scabs on both sides. So I needle my Red Sox fan uncle when they're down or my Yankee relatives when the reverse is true. But I have to admit, it's more fun to poke a stick at a Yankees fan (at least the ones I know), because they really don't take it well-most days!
I would say it must be hard to be a Yankees fan in Red Sox Nation, but I know most are too arrogant to notice.