Jackson and Sharpton do a lot of things that King did in the civil rights movement, maybe not 100% but nevertheless they did some very similar things. Today, any African Americans who stands up against racism against minorities and doesn't fall within the rightwing spectrum politically is called a race hustler. When Larry Elder makes a book called "Stupid Black Men and how to play the race card" the rightwingers don't see that as "race hustling" since Elder is a black rightwinger, if Jackson or Sharpton criticizes racism they're race hustlers. King, with his record of fighting against racism would be called a race hustler by today's rightwingers.
Well, there's a couple things to point at here...
First, your entire premise is based off nothing but an assumption. Specifically, that Martin Luther King Jr. would be fighting the exact same fight, in the exact same manner, in the same intensity as he did in the 1960's if he were alive in the climate today.
While in no way, shape, or form would I dare say that racism is gone from our country it would be an absolute falsehood to suggest that we're anywhere near a similar situation as we were at when Mr. King was speaking. Where as Sharpton and Jackson fight with a fervor one would expect for a 1960's civil rights crusader, there would be a possability that Luther could see the world today and feel a different tact could be taken to make the progress than was needed in 1960.
King seems the type that would have reasonable and honest understanding regarding the differences between the 60's and today. I think, more so than Jackson or Sharpton, King could and would acknowledge the many advances we've made and the good that's been done equally with combatting the issues still there. I think King would still have issues with incidents of police brutality, but would not so desire to disrespect those that came before by comparing the isolated incidents of today to the widespread systematic actions of yesterday.
Second, your premise is based off the notion that Luther is similar in style and view as the people like Jackson and Sharpton. I can not imagine, for a second, either of those two saying the following quoted piece of text in an honest, truthful, and sincere way:
But there is something that I must say to my people, who stand on the warm threshold which leads into the palace of justice: In the process of gaining our rightful place, we must not be guilty of wrongful deeds. Let us not seek to satisfy our thirst for freedom by drinking from the cup of bitterness and hatred. We must forever conduct our struggle on the high plane of dignity and discipline. We must not allow our creative protest to degenerate into physical violence. Again and again, we must rise to the majestic heights of meeting physical force with soul force.
The marvelous new militancy which has engulfed the Negro community must not lead us to a distrust of all white people, for many of our white brothers, as evidenced by their presence here today, have come to realize that their destiny is tied up with our destiny. And they have come to realize that their freedom is inextricably bound to our freedom.
We cannot walk alone.
The notion of having an issue with someone not being "authenticly black" seems foreign to King's views. The notion that we should vote for someone simply baesd on his race; or more specifically, that someone will or will not look after the interests of African Americans based singularly on race, again seems foreign to it. Where Jackson and Sharpton seemed focused singularly on making African-Americans better King seemed to be focused on true equality, on Blacks and Whites being equals and being brothers.
I have a dream that one day on the red hills of Georgia, the sons of former slaves and the sons of former slave owners will be able to sit down together at the table of brotherhood.
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I have a dream that my four little children will one day live in a nation where they will not be judged by the color of their skin but by the content of their character.
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-- one day right there in Alabama little black boys and black girls will be able to join hands with little white boys and white girls as sisters and brothers.
Jackson and Sharpton speak largely as dividers, seeking to prominence of their race more so than true equality. This is a striking difference from what it appears to be with King.
Thirdly, there's the base level of sincerity present. Jackson and Sharpton's lack of sincerity, their honest desire to truly fight for equality rather than just hype themselves up, self-promote, and push singularly for the advancement of their race all play into the view of them. Quite on the flip side, King gives off the impression that he is truly sincere in his struggles, doing it not for his own ego, self-interest, or singularly for "negros" but rather doing it out of a sense that it is right for America as a whole and beneficial to all people to strive for a place of equality between blacks and whites. This is evident in a variety of ways, largest of which perhaps the rhetoric and actions compared between the two.
Would King be massively well loved by the right of today if he was still alive? Probably not by many, because he'd likely still be very liberal and ideology on many issues there would be disagreements. However, I do not in any way believe he'd be lumped in with the Jackson's and Sharpton's of the world...rather, I could see him being much like a Democratic Colin Powel, an individual that the other side disagrees with and doesn't exactly loves but does respect.