Some background

This picture is posted multiple times every day on mainly /r/the_donald, but also Twitter and other media.

It is used to wave away that Trump is racist.

The point is to make Hillary Clinton look associated to the KKK, but the allegations are completely baseless.

To the left, it shows Hillary Clinton hugging Robert Byrd, a former Klansman.

Robert Byrd

Robert Byrd, a democratic senator from 1959 to 2010, was member of the KKK through the 1940s. In this period, he was heavily into this culture, and was very racist. No one denies that, not even himself.

In the 50s, he changed direction to the polar opposite: he changed to fighting segregation and institutionalized racism.

From his own words:

"I know now I was wrong. Intolerance had no place in America. I apologized a thousand times ... and I don't mind apologizing over and over again. I can't erase what happened."

Robert Byrd is an amazing person, who was able to turn from his original connections to something constructive. From 1970 and after, he spend a lot of time fighting for civil rights measures.

He was an outspoken critique of the Iraq War and the Bush administration.

Hillary Clinton and Barack Obama supports him

It is no secret. They support him.

"It is almost impossible to imagine the United States Senate without Robert Byrd. He was not just its longest serving member, he was its heart and soul. From my first day in the Senate, I sought out his guidance, and he was always generous with his time and his wisdom" -- Hillary Clinton

"He [Robert Byrd] was as much a part of the Senate as the marble busts that line its chamber and its corridors. His profound passion for that body and its role and responsibilities was as evident behind closed doors as it was in the stemwinders he peppered with history. He held the deepest respect of members of both parties, and he was generous with his time and advice, something I appreciated greatly as a young senator." -- Barack Obama

I would think this would be entirely uncontroversial, but Donald Trump and his supporters aren't known for representing things factually.

The right picture

The right picture is entirely fake and very misleading. It makes him seem to have been a Klansman in his later days, which is straight out false. He lost his affiliations in the 50's, as explained above.

Digging a little down, it becomes obvious. Look at the light, there are no proper shadows, which is the first indicies. If you zoom a little in, you easily notice that they failed with the background.

The head is taken from the very first result when searching from "Robert Byrd". Which can be seen by placing them over each other.

The outfit appears to come from a heavily enhanced picture of Daniel Carver, a "Grand Dragon of the KKK", who, ironically, is a Trump supporter.

Speaking of the KKK...

Fred Trump, Donald Trump's father, was arrested at a Ku Klux Klan rally in Jamaica, Queens. As a response to the HRC KKK meme, I made this for the lulz.

It is a little unfair to judge people based on their father's actions, so let's see what Trump himself thinks of the Ku Klux Klan:

Donald Trump refused to distance himself from David Duke, white supremacist and former Grand Wizard of the KKK, claiming that he knew "nothing about white supremacists". Even after he was told that he was a klansman, he refused to disaprove of him.

David Duke later compared Trump to Hitler..., as a complement.

Trump later reversed his position, due to the massive criticism. ^{much for "he tells it like it is"}

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TL;DR: The picture is fake, Byrd was member of the KKK when he was young, but turned away and fought against racism. You can choose between supporting somebody who supports one who was once a racist, or supporting an actual racist.

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Edit: Typos.

Edit: /u/throwaway111675 made this simple TL;DR in image form.