Well, you're assigning a motive to Lee here ("making a government institution look more moral") in a way that I would say is dubious: that this is how the result looks, sure, but I highly doubt Spike Lee sat down and thought "Cool story, but how can I make the police look better ?"...
IIRC, the way it's presented initially is that it's based upon "some fo' real shit", right ? That's not "This is a 100% historically accurate tale", right ? I guess you could say Lee should have used a different name for the main character because he changed the story significantly, I'd probably agree with that, but again, I don't think the film is really set up in a way that I would expect it to be exactly true to life. There is an argument to be made that because this story is not very well-known and because he does connect it to real life, there is a responsiblity there... we come back to the idea that you can expect exact historical truth from films, and I just don't think that's ever the case. A narrative film, by definition, doesn't adhere to the truth exactly, especially a film that wants to make clear political points. Admittedly, there is probably a limit to that type of reasoning, but I don't feel that BlacKkKlansman crosses it.
If Tarantino had done that with Inglourious Basterds, I dont really see how you could take it as anything else than a joke like the one in Fargo, so I'm not sure what the problem would have been there. It would have been misdirection more than anything else, I don't think these are comparable cases really.