LBJ was privately racist and mostly pro-segregation until 1963.
Well, he implemented the first civil rights bill since reconstruction in 1957 as a senator. The bill was weak, but not only because he knew he couldn't get more at the time.
Honestly, even if LBJ was privately racist (I assume he was but I only read the first two volumes of the Caro books a few years ago and my library didn't have the rest of the series, so I don't know. I could Google it, but I don't really care), his work on Civil Rights during his Presidency sort of negates whatever character flaws he personally had. Just like how George Wallace is evil for supporting and protecting segregation even though there is good evidence that he himself probably wasn't racist or at least not the to the degree of most of his supporters.
