This image is a mixture of fact and fiction. Lets break it down by claim.
First is the pictures of “Republicans”
From left to right, of Abraham Lincoln, Frederick Douglass, and Martin Luther King, Jr. Abraham Lincoln is known for being the first Republican President . Frederick Douglass was definitely a republican also, he made statements such as:
“I am a Republican, a black, dyed in the wool Republican, and I never intend to belong to any other party than the party of freedom and progress.”
He also made some fairly anti-Lincoln statements such as calling Lincoln “the white man’s president” and cited his tardiness in joining the cause of emancipation. He noted that Lincoln initially opposed the expansion of slavery but did not support its elimination. He also said in a speech “Though Mr. Lincoln shared the prejudices of his white fellow-countrymen against the Negro, it is hardly necessary to say that in his heart of hearts he loathed and hated slavery….” 
Next is… Martin Luther King Jr.
He was definitely not a Republican, and I’m not sure if he was put here in an attempt to make people believe something not true, or if it was an accident. King and his wife were pretty quiet about their political affiliations for the most part but here are some known facts about his party choices:
In a 1958 Interview King said: “I don’t think the Republican party is a party full of the almighty God nor is the Democratic party. They both have weaknesses … And I’m not inextricably bound to either party.” 
Martin Luther King III said in an AP Report that “It is disingenuous to imply that my father was a Republican” 
The King Center of Atlanta founded by MLK’s wife says he wasn’t a republican 
The King Center also said King didn’t officially endorse any party 
Kings niece Alveda King said he was, then said: “I regret having said to a group of peers that my Uncle M. L. (Dr. Martin Luther King, Jr.) was a Republican. I said that without having all the facts.” 
King had said himself in his autobiography: I always voted the Democratic ticket. 
Kings wife said they didn’t identify with either party
there is no evidence that he registered republican
Throughout the Civil Rights movement he worked with the northern Democratic Party
Next on the list is “Republicans abolished Slavery”
This is mostly true, as the Republicans in the House and Senate had majorities and had most of the passing votes. The senate vote was 38 to 6, with 34 Republican votes, 3 Democrat votes, and 1 Unconditional Unionist vote [votes]
The house vote was 119-56, with 84 Republicans voting for, 14 Democrats for, and 49 Democrats voting against with another 8 not voting. [vote] Clearly very few Democrats supported it, but a few still did.
Next is “Republicans Gave Blacks the Vote”
The The Voting Rights Act of 1965 was jointly sponsored by a Democrat and Republican (Senate Majority Leader Mike Mansfield (D-MT) and Senate Minority Leader Everett Dirksen (R-IL)) at a time when Democrats had a filibuster proof Senate. Initially, Dirksen did not intend to support voting rights legislation, but President Johnson enlisted Dirksen to help gain Republican support. The finals votes where definitely a Democrat effort with some Republican help.
The Final senate vote was 77-19 with 47 Democrats and 30 Republicans voting for, and 16 Democrats against and 2 Republicans voting against. [vote]
The Final House vote was 333-85 with 221 Democrats voting for it, and 111 Republicans voting for it, and 62 Democrats voting against and 23 Republicans voting against. [vote]
The Republicans Passed the Civil Rights act
The Civil Rights Act of 1964 was President Kennedy’s idea and the Senate had a Democratic Majority. Senate Minority Leader Everett Dirksen (R-IL) and Senate Majority Leader Mike Mansfield (D-MT) both voiced support for the president’s bill and was initially introduced in the House as H.R. 7152 by Emanuel Celler (D–NY) . While it would not have likely passed without some Republican support, it was written by Democrats, introduced by Democrats, and passed in Democrat Majority house and senate with a majority of Democrat votes, and signed by a Democrat President.
The Final Senate vote was 73-27 with 46 Democrats, 27 Republicans voting for, and 20 Democrats, 7 Republicans voting against. [vote]
The Final House vote was 290-130 with 152 Democrats, 138 Republicans voting for, and 96 Democrats, 34 Republicans voting against. [vote]
First Black Republican Senator
Though the date is off by one year, Hiram Rhodes Revels took office in 1870, as the First Black Republican Senator.
First Black Democrat Senator
Carol Moseley Braun was the first black Democrat voted into senate, in 1999.
50% of Black Senators have been Republican
There have been 9 Black Senators in office, 4 Republicans, and 5 Democrats 44% Republican, and 55% Democrat. All 5 Democrats have been elected since 1999, but only one Republican in the same time, with the other 3 being in the 1800’s, and 1960’s.
The First 22 Black Representatives
The first 21 black Representatives were Republicans, #22 was Democrat Arthur Wergs Mitchell. This is still mostly true though, however the next 42 in a row and 105 out of 127 total (83%) have been Democrats.
 The Presidents of the United States of America,” by Frank Freidel and Hugh Sidey. ( 2006 )
 David W. Blight, Frederick Douglass’ Civil War: Keeping Faith in Jubilee (1989)
 The Martin Luther King, Jr. Papers Project
 Associated Press, July 4, 2008
 The National Journal July 12, 2008
 Alveda King’s Blog
 Twitter / Alveda King
 The Papers of Martin Luther King, Jr, page 384