Frankly, no. Not only can Yankees and Red Sox fans not get along, they should also avoid any measure that might possibly lead to anyone getting along. It took two state militias to break up the Hatfield's and McCoy's, and nothing short of another state-backed intervention should cause a truce in this storied sports rivalry.
This perspective, of course, is against the common sensibilities that allow a society to thrive. Reconciliation and compromise are fundamental elements of our democracy—not in our actual government, mind you, more in theory, really—and so, to appear to promote the notion that no common ground exists is to appear to promote anarchy. Put that way, well, let anarchy reign.
Many would say, of course, that there is enough conflict in the world. We are not living in a time that can be referred to as politically stable, not domestically or globally, really, so to suggest that any conflict be continued is by no means a positive contribution to the greater good. It must be said, however, that certain struggles are sacred, perhaps even healthy in a big picture kind of way, and the Yankees-Red Sox rivalry certainly qualifies as such a struggle.
It could be said that the inherent differences between the two organizations are what make the rivalry so necessary and vibrant. It is essentially your classic "opposite sides of the tracks" struggle, the uptown vs. downtown thing. If this were music, it would be the boy band vs. the garage band, with the Yankees of course being the well-manicured, highly-structured boy band, and the Sox taking on the role of the grungy, unkempt neighborhood rocker. If anyone on either side of the equation is offended by that, well, too bad, this is war.
The Yankees, of course, have experienced the same kind of success that the well-managed boy band often does. The difference, of course, is that the Yankees are the boy band that never fades away, never loses touch with its audience or its ability to produce hits, if you'll pardon the pun. The Red Sox identity, by comparison, is the quintessential garage band in that they're always firing away, always pressing the gas, and always unconcerned with how they look while trying.
The organizational differences are truly manifested in the public identities of the players each team develops and pursues.
Where the Yankees have a CEO-type at shortstop as their leader, cool, understated, in control, the Red Sox have an iron-worker at second base as theirs, immune to danger, balanced between the reckless and the heroic. Where the Sox have a plumber at third, the Yankees have, literally and, for the most part, practically, the prototypical hedge fund manager. It's white collar vs. blue collar, and it's a wonderful thing to behold.
If you speak with fans of each team, it is these differences in identity that fuel the feud as much as wins and losses. The typical Yankees fan would like nothing more than to poke Dustin Pedroia in the eye or trip Kevin Youkilis as he's walking down the street. Similarly, on sight alone, Derek Jeter and Alex Rodriguez have the ability to induce the every day Red Sox fan to violently discharge their most recent meal. Though there is a healthy respect for the respective abilities of each, this respect takes a back seat to the less civil emotions every time.
In a true sense, it should always be this way. No Yankee should ever strive to leave the figurative executive suite any more than any Red Sock should aspire to leave the metaphorical factory floor. There is great honor in each identity, in professional sports, and more so in our every-day lives, and the coming together of these identities in conflict is, in fact, the highly-sought-after common ground we hear so much about.
So let anarchy reign. Allow yourself to revel in every moment of angst and frustration that comes about. Know that, as a fan of the Yankees or Red Sox, you are part of something very special, a conduit, really, to a realm where nothing else needs to matter for three of four hours at a time.
And while you might be motivated to separate yourself from your last meal after a two-out RBI single from Derek Jeter, or find yourself searching for a sharp stick in the event you run into Dustin Pedroia somewhere after he hits one over the Monster, consider yourself very fortunate just to be part of that realm.
It is a distinction that very few enjoy, but that very many envy.