Today being the MLK holiday, we can be sure that some of the Republican presidential candidates will have nice things to say about Dr. King, and they will trot out the old “content of their character” MLK quote to suggest he was a conservative.
Although King did not formally endorse any presidential candidates, he came very close on occasion, and it’s instructive to recall some of his thoughts on Republican presidents and candidates during his lifetime. On Eisenhower:

In September 1957 I thought it was quite regrettable and unfortunate that young high school students in Little Rock, Arkansas, had to go to school under the protection of federal troops. But I thought it was even more unfortunate that Arkansas Governor Orval Faubus, through irresponsible actions, left the president of the United States with no other alternative. I believe firmly in nonviolence, but, at the same time, I am not an anarchist. I believe in the intelligent use of police force. And I thought that was all we had in Little Rock. It wasn’t an army fighting against a nation or a race of people. It was just police force, seeking to enforce the law of the land. It was high time that a man as popular in the world as Eisenhower-a man with his moral influence-speak out and take a stand against what was happening all over the South. So I backed the President, and I sent him a telegram commending him for the positive and forthright stand that he took in the Little Rock school situation. He showed the nation and the world that the United States was a nation dedicated to law and order rather than mob rule.
Nevertheless, it was strange to me that the federal government was more concerned about what happened in Budapest than what happened in Birmingham. I thought Eisenhower believed that integration would be a fine thing. But I thought he felt that the more you push it, the more tension it would create, so, just wait a few more years and it will work itself out. I didn’t think that Eisenhower felt like being a crusader for integration. President Eisenhower was a man of integrity and goodwill, but I am afraid that on the question of integration he didn’t understand the dimensions of social change involved nor how the problem was to be worked out.

On Goldwater:

The Republican Party geared its appeal and program to racism, reaction, and extremism. All people of goodwill viewed with alarm and concern the frenzied wedding at the Cow Palace of the KKK with the radical right. The “best man” at this ceremony was a senator whose voting record, philosophy, and program were anathema to all the hard-won achievements of the past decade.
It was both unfortunate and disastrous that the Republican Party nominated Barry Goldwater as its candidate for President of the United States. In foreign policy Mr. Goldwater advocated a narrow nationalism, a crippling isolationism, and a trigger-happy attitude that could plunge the whole world into the dark abyss of annihilation. On social and economic issues, Mr. Goldwater represented an unrealistic conservatism that was totally out of touch with the realities of the twentieth century. The issue of poverty compelled the attention of all citizens of our country. Senator Goldwater had neither the concern nor the comprehension necessary to grapple with this problem of poverty in the fashion that the historical moment dictated. On the urgent issue of civil rights, Senator Goldwater represented a philosophy that was morally indefensible and socially suicidal. While not himself a racist, Mr. Goldwater articulated a philosophy which gave aid and comfort to the racist. His candidacy and philosophy would serve as an umbrella under which extremists of all stripes would stand. In the light of these facts and because of my love for America, I had no alternative but to urge every Negro and white person of goodwill to vote against Mr. Goldwater and to withdraw support from any Republican candidate that did not publicly disassociate himself from Senator Goldwater and his philosophy.
While I had followed a policy of not endorsing political candidates, I felt that the prospect of Senator Goldwater being President of the United States so threatened the health, morality, and survival of our nation, that I could not in good conscience fail to take a stand against what he represented.

On Reagan:

…When a Hollywood performer, lacking distinction even as an actor can become a leading war hawk candidate for the Presidency, only the irrationalities induced by a war psychosis can explain such a melancholy turn of events.

King was more ambivalent about Nixon, who had called King “frequently about things.” King said of Nixon that “it is quite possible that he has no racial prejudice,” and “is absolutely sincere on this issue,” but also that he also considered Nixon a “moral coward” for not taking a strong moral stand on civil rights at a time when it would have helped a lot. (from chapter 15 of “The Autobiography of Martin Luther King, Jr.”)
None of this is to say that there were no progressive Republicans who supported the African American freedom struggle –there were some like Senator Jacob Javitz and Gov. Nelson Rockefeller. Interestingly, Republicans including Sen. Goldwater, William Buckley, Sen. Strom Thurmond and President Reagan supported the King holiday bill, despite their stated opposition to the Civil Rights Act of 1964. Rep. Jack Kemp was instrumental in passing the MLK holiday legislation. There are many rank and file Republicans who admire and celebrate Dr. King today.
In a transparent attempt to back away from his repulsive newsletter, Rep. Ron Paul has recently lauded what he sees as King’s libertarian creds. But Paul opposed both the Civil Rights Act of 1964 and the MLK holiday.
And yes, there were plenty of racist Democrats during King’s lifetime. It would be fair to say that racial prejudice was a defining characteristic of too many Dixiecrats.
King never gave up hope that both parties would take a strong stand against racial discrimination, and he testified to the platform committees of both major parties. But the record clearly shows which political party today is the more vigorous champion of the cause of racial and economic justice championed by Martin Luther King, Jr.