OF COURSE, IT'S NOT AS SIMPLE as Truman = Good, Thurmond = Evil. (Well, mostly it is, actually, but only to a first approximation.) LincolnPlawg has a lot of interesting history, including a statement from Harry Truman that he opposed an anti-lynching bill, but would have to vote for it if it came up for a vote, and a letter from Eleanor Roosevelt (with a GIF) reporting that FDR thought federal involvement in anti-lynching efforts was a violation of states' rights. (Given FDR's blithe unconcern for the niceties of federalism, this seems like, well, an excuse. Or a lie, if you prefer.)
What's astounding from a modern perspective is how deeply racist many figures regarded as "progressive" today were. Oliver Wendell Holmes' support for eugenics, shared by many Progressives, is only one example, if an especially appalling one.