Calling someone a douchebag is an insult. Calling someone a racist is basically calling them evil.
Racism is the United States's Original Sin. The mistaken belief that black people were/are less than whites was/is used to justify inhuman treatment of our black American brothers and sisters. It was used to justify chattel slavery, efforts to disenfranchise freed slaves after the Civil War, Jim Crow, assassinations and terrorism, and current efforts to marginalize black Americans politically. Calling someone a racist is a shorthand of saying you support some or all of those horrors. Being an overt racist has actually become so toxic that white supremacists have had to totally pivot their language and behavior away from things like the N-word (to thug, All Lives Matter, etc.) and public demonstration (away from KKK marches and toward nearly completely online efforts).
Because deploying a charge of racism is almost a super-accusation, it needs to be used carefully. People won't take the charge seriously if it's used casually to describe anything negative that happens to a black person. I think that hurts others who would make the same claim except with much more evidence and in a more grounded and level-headed way. Because it lets people with an actual racist agenda say things like: "See? Racism doesn't exist!" or "Those cops who killed that unarmed person couldn't have been racist, racism isn't real." etc.
That's why, IMO, Pippen should have said something else about Jackson. Attacked his temperment or just called him a jerk. Because I agree with you, that's what Pippen was trying to do, and by calling Jackson a racist over a single incident that was on its face not at all racist, he made himself look like an ass and potentially hurt real and credible accusations of racism.