Your analogy is a good one -- Dr. King acknowledging how there was a certain breed of White person who'll never get onboard with Black and Brown people, and, instead, his arguments were alternately directed toward White people who *could* potentially be swayed to support equality but who were usually ignorant about the realities of systemic injustice faced by BIPOC communities.

He was essentially dissecting the proclamations of white supremacists in order to illustrate the morality of black equality (and, more generally, BIPOC equality).

Yes, this is indicative of how there are often MORE than just two "sides" to a given issue.

I don't argue simply to be contrarian. I don't like to argue. I argue out of necessity, when someone is displaying inanity.