Quite racist. J. Edgar Hoover was born in 1895, and brought up in Washington D.C. At the time Washington D.C. was a strictly segregated city, and Hoover seems to have absorbed a lot of racist attitudes.

In 1919 Hoover began working for the Bureau of Investigation, and his job was to monitor and disrupt the work of American left-wing radicals. During this period (1919-1920), there were huge race riots in many cities, caused by the Great Migration of blacks seeking better jobs and opportunities unavailable in the South, and racists attacking them in response. Hoover thought that many of these riots were caused by subversive agitators, and that black people were largely to blame for them.

In the 1950s, when Hoover was director of the FBI, he established a "dirty tricks" program called COINTELPRO. This program was used to disrupt various organizations he considered subversive and un-American, and its methods included illegal wiretapping, infiltrating organizations, spreading false rumors, forging documents, and burglary. Martin Luther King Jr. was one of its main targets, as were other civil rights leaders and organizations.

In 1964, at a press conference, Hoover denounced King as "the most notorious liar in this country." And one of his deputies, William Sullivan, sent a letter to King calling him a "a colossal fraud and an evil, vicious one at that." The letter encouraged King to stop being a civil rights leader and possibly to commit suicide. The text of the letter is here: http://genius.com/Federal-bureau-of-investigation-uncensored-suicide-letter-to-mlk-annotated

And under Hoover's direction, the FBI did not aggressively investigate civil rights violations. When three civil rights workers were murdered in 1964, Lyndon Johnson had to put pressure on Hoover to investigate.

So, to sum up, Hoover was quite racist. He had no sympathy for American blacks or the civil rights movement, thought black people were inferior, and looked favorably on segregation. Hoover definitely had a vendetta against King. While some black groups and leaders (such as the Black Panther Party and Malcolm X) favored using violence to achieve their goals, Martin Luther King Jr. remained steadfastly devoted to nonviolence (and was mocked by some groups for his position). This, in my opinion, implies that Hoover's surveillance of King wasn't motivated by a fear of domestic terrorism, but instead by antipathy to racial equality.

Sources: "What an Uncensored Letter to M.L.K. Reveals." http://www.nytimes.com/2014/11/16/magazine/what-an-uncensored-letter-to-mlk-reveals.html?_r=0

Young J. Edgar: Hoover and the Red Scare, 1919-1920. Kenneth Ackerman. 2011.

Parting the Waters: America in the King Years, 1954-1963. Taylor Branch.

Pillar of Fire: America in the King Years, 1963-1965. Taylor Branch.