RFK was really overrated when it came to civil rights.
Please watch the documentary "Freedom riders". RFK called the Freedom Riders foolish, and thought they deserved to be taught a lesson (apparently for making him and his brother look bad) when the Mississippi police arrested them. He only really began to care about civil rights when he realized that not doing anything made him look bad.
Also, lets not forget that his brother gave speeches to segregated (white only) audiences in the South while other prominent Democrats such as Stuart Symington refused to do so.
Ted was the only truly liberal Kennedy, fully capable of articulating progressive positions (because there's more to being a good politician than casting a vote) but he had his demons too.
Not to mention he ordered the FBI to wiretap MLK.
As of JFK, as Senator he voted for the bill that let the state courts try (and naturally acquit) those who prepeared and/or participated in lynchings. This bill was strongly opposed by the people such as Humphrey and Symington.