I realize I'm a little late to this party, since the movie came out in April, but better late than never.
The movie covers the events that lead up to Jackie Robinson being the first baseball player to break the color line and his Rookie of the Year 1947 season. I knew the general outline of the story from baseball history I've read. I suspect that the movie pulled some punches here. Certainly there are some ugly representations of racism here but the movie would have you believe that Robinson came to be accepted by the end of the season. I read Hank Aaron's biography last year and even in 1954, when Aaron came up to the majors, black players were still not really accepted.
As a Phillies fan, I was appalled that the movie chose to use the Phillies as the most vocal representation of the racism of other players. Appalled but I guess not surprised. The Phillies were, after all, the last NL team to desegregate (finally in 1957). The Phillies manager, Ben Chapman, into whose mouth the most racist statements were put, was not fired after the 1947 season (although the team's 62-92 record would have justified it) as implied in the movie, but during the 1948 season. He did never work as a manager again. Chapman and Robinson ended up appearing in a photo together to imply hatchets buried. Here's the actual photo.