I came across this contemporary political cartoon today (with commentary by the original owner of the newspaper copy, presumably). A cursory Internet search prompted by the cartoon revealed this MLK quote from a speech he made in September 1967:
Urban riots must now be recognized as durable social phenomena. They may be deplored, but they are there and should be understood. Urban riots are a special form of violence. They are not insurrections. The rioters are not seeking to seize territory or to attain control of institutions. They are mainly intended to shock the white community. They are a distorted form of social protest. The looting which is their principal feature serves many functions. It enables the most enraged and deprived Negro to take hold of consumer goods with the ease the white man does by using his purse. Often the Negro does not even want what he takes; he wants the experience of taking. But most of all, alienated from society and knowing that this society cherishes property above people, he is shocking it by abusing property rights. There are thus elements of emotional catharsis in the violent act. This may explain why most cities in which riots have occurred have not had a repetition, even though the causative conditions remain. It is also noteworthy that the amount of physical harm done to white people other than police is infinitesimal and in Detroit whites and Negroes looted in unity.
King speaks favourably about violent protest without directly endorsing it ("they may be deplored", he begins). And yet many or most of the "pro-MLK" sources I can find - the MLK Encyclopedia on Stanford University's website, for instance - greatly emphasize King's commitment to nonviolent resistance and draw attention to the influence of "Gandhi's legacy" on him following his 1959 visit to India.
So what's going on here? Can anyone provide more depth and nuance to this for me? Did King encourage or condone violence, theft, and destruction, or not?
No, he says they are deplored. They being violent urban riots. Do you have any examples of him speaking favorably about violent protests? When you just claim he has, that is a strawman. MLK is a historically noted pacifist. Extraordinary claims required extraordinary evidence.