(1) There's not only no evidence Cobb was a racist, there's in fact a lot of evidence that he had very progressive ideas on race for men of his era and regarded them more or less as equals, or at least that race didn't put him above them. He enthusiastically supported integration of the big leagues and praised black ballplayers. One of several blacks employed by Cobb, Alex Rivers, named his son after the ballplayer and said, “I love the man.” His father, something of a public intellectual, once put a stop to the planning of a lynching and was "an outspoken advocate for the public education of black Americans."
(2) A catcher on the Tigers in 1907 was in a badmouthing campaign to get Cobb traded, so he made up various stories about Cobb (e.g. that he assaulted a black groundskeeper
and his wife), and also "had a habit of beating up Cobb"
(3) He went well out of his way to be kind to the powerless, including sheltering a 16yo ballboy, in an era when ballboys were badly mistreated, even to the point of letting him share Cobb's room in (segregated) hotels. It's quite a story, halfway through the article... parable-grade Good Samaritan-ing. He would write multi-page letters in response to fan mail.
(4) In 1909, Cobb got into a fight with the (white) security guard at a hotel, which involved Cobb getting him across the wrist with a pen knife. Cobb later pled guilty to assault and paid a fine and settlement. Charles Alexander's 1984 biography invented that the guard was black, when Leerhsen's research proved he wasn't, and no contemporary accounts had said otherwise. Sometimes this story is distorted into "stabbing a black waiter for 'being uppity'." Cobb did once climb into the stands to argue with a black fan, and another time beat up a (white) heckler; fights between players and fans were common in that day, the article cites many examples.
(5) After retirement he became a significant philanthropist. He funded a
hospital, started a college-education fund for kids, and funded the latter with a quarter of his estate at his death.
(6) His general hotheadedness did cost him, in divorces and friends - something he regretted at the end of his life. He was unpopular with a lot of his teammates in his early career, including Sam Crawford who was initially a mentor to him. He was estranged from one of his sons, who had flunked out of both Princeton and Yale for alcoholism. But he had 150 people show up to his funeral, including his first wife of 39 years, and was friends with a number of his ballplayer contemporaries.