Most answers acknowledge that the use of blackface in the movie has a self commenting and satirical nature to it, as evidenced by the context in which the acting unfolds: The person in question is a deep method actor and his use of blackface is the ultimate extreme to which he goes in his misled conviction to give his best performance.
The use of black face is knowingly done to criticize the practice, which is evident both to the audience by the way it is portrayed as a struggle of the white actor to imitate African American slang and mannerisms, and to the movie characters themselves via diegetic commentary on the subject where it is continuously acknowledged that it is the wrong thing to do.
This absolves the movie of any offensive authoral intent, and as a matter of fact serves as the root of much of the comedic success of the movie.
Outside the movie, Brandon T. Jackson (the black actor most involved in the blackface-centric scenes), as well as the NAACP were approached with the script prior to the movie release to make sure the material was handled sensibly.
There is therefore ample evidence that there was no harmful intention in the use of blackface and as such Robert Downey Jr is not deserving of any criticism for it.
In the own words of the movie: