Carl Everett
Carl Everett only played in Boston for a couple of seasons and his first season in 2000 actually went really well. He made the All-Star team and posted a .959 OPS in 561 plate appearances. He did struggle more the following season partially due to an injury, but he still put up a reasonable .761 OPS in 2001. He also very firmly did not believe in dinosaurs, but that is more funny than a reason to hate the guy.
So why is Everett on the list? Well, to be blunt, Everett wasn't well-liked by many people at all. He got a suspension for bumping an umpire which is a big no-no, had a very adversarial relationship with the Boston media, and is generally regarded as one of the biggest clubhouse cancers of all-time. A quick look at his Baseball-Reference page show that he never played more than three years with any organization and given his reputation as kind of a jerk, it is not hard to see why.
Babe Ruth
This one is rooted in the annals of baseball history. Very famously, Babe Ruth started his career with the Red Sox and when Boston's owner ran into financial trouble and Babe wanted to make more money, the Red Sox sold him to the Yankees. The rest of the story everyone knows. Ruth would go on to be arguably the best baseball player to ever live while Boston had the Curse of the Bambino placed upon them and had to wait many decades to find championship glory again.
This one does feel a bit unfair as Ruth certainly deserved to be well-compensated even back then and it was ultimately ownership's decision to ship him off to the Yankees. However, the sting of Babe being the centerpiece in probably the worst transaction of all-time is still too much for many Red Sox fans to ignore especially when they suffered so long afterwards.