Max O'Connell’s review published on Letterboxd :
How to make a non-ossified biopic about an inherently noble cause/person:
1. Focus on one small part of the character's life.
2. Focus on the backroom deals, the horse-trading, the deal-making and the compromises needed to make progress.
3. Cast an actor who's as good a listener as David Oyelowo, who's commanding without ever feeling pre-bronzed because he's constantly leaning in to what everyone's saying and weighing information.
4. On top of that, get someone like Ava DuVernay to direct, as she'll get the least-showy performances out of both actors that tend to show off (Cuba Gooding, Jr., Giovanni Ribisi) or characters that beg actors to to give show-stopping performances (George Wallace, LBJ). Everything is perfectly measured, and with the exception of Martin Sheen as the world's most dignified judge, none of the stars are particularly distracting (also: props to Oprah for never making scenes about her even in movies that seem to encourage it, a la The Butler).
5. Show the violence honestly without ever lingering too much on the brutality, instead showcasing how it affects the people and how they'll have to adapt (or not).
6. When dealing with questions of whether or not the film's noble center was a flawed man, don't dodge the issue (here, it's MLK's philandering). Show how it hurt the people around them. At the same time, show how it's just one facet, not an all-consuming problem, and that it's insignificant compared to the work he did.
EDIT: wrote more at Criticwire.