One surefire way to not endear oneself to Boston fans is to look like you are phoning it in and essentially try to wait out the end of a contract and that was what Roger Clemens did. The last two years Clemens was in Boston, he did not look to be in as good a shape and Clemens famously did not like that Boston viewed his next contract as playing out the "twilight of his career". Clemens refused to sign with the Red Sox again after the 1996 season and ended up going to the Blue Jays.
However, it doesn't end there. Not only did Clemens spurn the Red Sox, but he eventually would join the hated New York Yankees which is pretty much a black mark forever for Red Sox fans. Clemens also had a reputation for being an incredibly surly person to deal with and also has the cloud of rumored PED usage hanging over him. In short, he doesn't have a lot of fans in Boston at the moment.
Wil Cordero isn't a name that many Boston fans would immediately call out, but he deserves some special recognition. Cordero only played two seasons in Boston with one of those seasons getting shortened significantly due to a couple injuries. Not exactly what you want to see out of a former All-Star, but playing a couple meh season in Boston isn't what gets him on the list.
What gets him there is multiple domestic violence arrests including him pleading guilty to assault and battery of his wife in 1997. The rules for dealing with player misconduct were different back then and it is safe to say that given Cordero was arrested multiple times in his career, it is likely he would have been bounced from the league much more quickly if he played nowadays.