The New York Times editorial board explains the politics behind Republican posturing about the Black Lives Matter movement, and calls out several of their presidential candidates in particular for trying to stir up white resentment:

The Republican Party and its acolytes in the news media are trying to demonize the protest movement that has sprung up in response to the all-too-common police killings of unarmed African-Americans across the country. The intent of the campaign — evident in comments by politicians like Gov. Nikki Haley of South Carolina, Gov. Scott Walker of Wisconsin and Senator Rand Paul of Kentucky — is to cast the phrase “Black Lives Matter” as an inflammatory or even hateful anti-white expression that has no legitimate place in a civil rights campaign.
Former Gov. Mike Huckabee of Arkansas crystallized this view when he said the other week that the Rev. Dr. Martin Luther King Jr., were he alive today, would be “appalled” by the movement’s focus on the skin color of the unarmed people who are disproportionately killed in encounters with the police. This argument betrays a disturbing indifference to or at best a profound ignorance of history in general and of the civil rights movement in particular. From the very beginning, the movement focused unapologetically on bringing an end to state-sanctioned violence against African-Americans and to acts of racial terror very much like the one that took nine lives at Emanuel African Methodist Episcopal Church in Charleston, S.C., in June.
The civil rights movement was intended to make Congress and Americans confront the fact that African-Americans were being killed with impunity for offenses like trying to vote, and had the right to life and to equal protection under the law. The movement sought a cross-racial appeal, but at every step of the way used expressly racial terms to describe the death and destruction that was visited upon black people because they were black.

It’s a shameful legacy for a political party which once included leaders who actively supported civil rights reforms. Republicans like Sens. Jacob Javitz, Lowell Weicker, and Everett Dirksen, Governor Nelson Rockefeller and others all had impressive records of supporting racial justice and equality, even though they were conservative on most economic issues. Today GOP leaders are all active and tacit supporters of suppressing of African American votes. Huckabee has even advocated illegal measures to suppress voting on several occasions.
In reality Dr. King and the Movement were deeply concerned about violence targeting Black Americans and spoke out about it many times. As the Times editorial notes, in his eulogy for the four little girls who were killed in the Birmingham church bombing in 1963, Dr. King “did not shy away from the fact that the dead had been killed because they were black, by monstrous men whose leaders fed them “the stale bread of hatred and the spoiled meat of racism.” He said that the dead “have something to say” to a complacent federal government that cut back-room deals with Southern Dixiecrats, as well as to “every Negro who has passively accepted the evil system of segregation and who has stood on the sidelines in a mighty struggle for justice…”
The Times editorial also emphasizes the clear connection between voter suppression and the racial violence that occurred during the Movement:

During this same period, freedom riders and voting rights activists led by the young John Lewis offered themselves up to be beaten nearly to death, week after week, day after day, in the South so that the country would witness Jim Crow brutality and meaningfully respond to it. This grisly method succeeded in Selma, Ala., in 1965 when scenes of troopers bludgeoning voting rights demonstrators compelled a previously hesitant Congress to acknowledge that black people deserved full citizenship, too, and to pass the Voting Rights Act of 1965. Along the way, there was never a doubt as to what the struggle was about: securing citizenship rights for black people who had long been denied them.

During the Civil Rights Movement most southern Democratic elected officials were a huge part of the problem of racial injustice and they worked together with right-wing Republicans to relentlessly suppress the votes and civil rights of African Americans. It was a coalition of progressive Democrats and Republicans who opposed and finally overcame them to secure passage of the great Civil Rights reforms of the sixties.
But the Democratic Party has matured to the point where no Democratic political leaders advocate voter suppression or rolling back the clock on civil rights. Conversely, with very rare exceptions, no Republican leaders oppose voter suppression and most of them actively support it.
The Times editorial goes on to underscore the fact that Black Lives Matter “focuses on the fact that black citizens have long been far more likely than whites to die at the hands of the police, and is of a piece with this history.”
They are not saying that white lives don’t matter; they are calling needed attention to the outrage of racially-motivated violence, committed by police and others, and they are demanding corrective action, in keeping with the best traditions of the American Civil Rights Movement. And despite media focus on riots and civil disturbances in the wake of police violence, the overwhelming majority of Black Lives Matter protesters have remained exclusively nonviolent.
Republicans are trying to suggest otherwise. But this lie won’t stand the test of honest scrutiny.
The modern Republican Party now sees its hope for survival being based on energizing white resentment toward people of color, particularly those who dare to protest for their basic civil rights. As the editorial concludes, “politicians who know better and seek to strip this issue of its racial content and context are acting in bad faith. They are trying to cover up an unpleasant truth and asking the country to collude with them.”
The Republicans have deployed this strategy for decades with mixed results. But it is especially shameful when directed at a group of citizens whose central concern is their right to be free from racially-motivated violence.