I'm not sure who had the idea to put Sweet Caroline, but this is absolutely not Mr. Neil Diamond's fault . I like Neil Diamond's work, he has a great voice, hehehehe anyway...
IMO, The thing is that you shouldn't be that happy while your team is falling in pieces, that's the point and make sense. Nevertheless, I think some people goes to the stadium in order to spend some fun time with their families and forget real life for a while. I don't see anything wrong on that. Some fans take this team very seriously and as a part of their daily life(maybe like some of us) and some not that much, I don't have a problem with that either. Are they pink hats?, which fan is better? Nobody can't measure and judge that. Each fan expresses his/her sympathy in so many different ways, so...
Anyway... put whatever song or performance you want, that's not the issue IMO. Our issues go beyond Sweet Caroline, that's for damn sure my friends.