The problem with the premise is the definition of
racism. It seems to bifurcate when comparing racism of the 60s to the "racism" of today. As an example, segregation and "separate but equal" laws are trivially racist by the textbook definition, but "systemic racism" is a nebulous term.
If we choose a definition of systemic racism consistent with the radicals in the protests he may very well agree with it. There's no saying for sure without injecting your own biases into the statement. I haven't studied the marches in the 60s well enough to understand his total stance. I do know he was strongly anti-capitalist in his later years.
That being said according to
this he had no obvious political leanings with his one goal being civil rights. Though it's been assumed he was a democratic socialist. If we project him in that lens he may be somewhat closer to a Bernie Sander at least as a first order approximation.
I don't believe he would support the race riots based on his writing knowing he preferred non-violent civil disobedience. I don't believe he would support the rise of BLM to the status of a political party, nor do I believe he would support the overt kowtowing of every BLM mantra by the media:
https://books.google.com/books?id=qW-NYdIefPgC&pg=PA84#v=onepage&q&f=false
Actually, the Negro has been betrayed by both the Republican and the Democratic party. The Democrats have betrayed him by capitulating to the whims and caprices of the Southern Dixiecrats. The Republicans have betrayed him by capitulating to the blatant hypocrisy of reactionary right wing northern Republicans. And this coalition of southern Dixiecrats and right wing reactionary northern Republicans defeats every bill and every move towards liberal legislation in the area of civil rights.
Given this I don't believe he would support Biden nor would he support Trump. He would likely view the Democrat's position as a facade given by their sudden and immediate appreciation of all things Black in an election year and their over-the-top prostration. He would, in my opinion, outwardly oppose Biden due to his being against integration. I think he would view the Republican position as hypocritical (Republicans generally supported civil rights legislation) given there has been almost nothing from their side w.r.t. police violence.
Would he support the protests in light of the
context of the shootings? It's hard to say without imposing my own view on him. But if his historical position is accurately portrayed I do not believe he would support such a sudden and visceral reaction to the death of criminals (in the literal sense of the word: having committed a crime). This context is
far different than the context given in the 60s where young, innocent, black men were being
literally lynched and
innocent Black people were being kept "separate but equal".