IMO the term 'Pink Hat' has come to be tossed around too loosely and in fact is misunderstood and misused by some of the posters here. It's a pet peeve of mine, I guess.
I'm willing to be corrected on this, but my understanding of the term 'Pink Hat' is that it refers to the bandwagon fans who jumped on board with the Red Sox in 2004, or after 2004, when it became cool to be a Sox fan. I think it especially refers to fans who knew little about baseball or the history of the Sox, and who wanted to be in Fenway because it was a happening place. The type who would be grinning and singing 'Sweet Caroline' even if the Sox were losing by 5 runs. And of course the type who would think a pink Red Sox hat looked good on them, or their girlfriend.
Presumably, most or all of these 'Pink Hats' have deserted the team by now.
A 'Pollyanna' fan is something completely different. A Pollyanna is a fan who tries to look on the bright side of things most of the time. They don't wear a pink hat but they might be accused of wearing rose-colored glasses.
As opposed to a Pink Hat, though, a Pollyanna can be a long-term, loyal Red Sox fan who knows all the history and has suffered, but is just positive by nature.
I'm much more of a Pollyanna since the Sox won the Series twice. I've been with the team since 1969, and until 2004 my dream was to see them win it once, and it was starting to look like it might not happen in my lifetime. So that changed my whole perspective.
I don't mind being called a Pollyanna, but to me it's a huge insult, and dead wrong, to call me a Pink Hat.