LBJ advocated for and signed the landmark legislation of the civil rights movement and spearheaded a massive expansion of the welfare state through the Great Society. He did all this despite being a Southern Democrat and being quite racist in private. Why was LBJ so liberal compared to his southern colleagues, and why was he able to get so many said colleagues on board with his liberal legislation? The stereotype of Southern Democrats is that they were a bunch of staunch conservatives whose Democratic identity was driven mostly by persisting Civil War era grievances. Is this picture inaccurate, or was LBJ just so politically talented that he was able to wrangle the southern caucus where others had failed?
Lyndon Johnson was hardly unique, though unusual. Democrats from the South were not monolithically conservative so much as in the South basically the entire political spectrum was contained within the Democratic Party because of the Republican Party's near-total irrelevancy. (This changed faster in Texas than elsewhere, as Eisenhower carried Texas in 1956 and John Tower became the first Republican Senator in 50 years in 1961 when he won the special election for the seat LBJ vacated...Texas was already drifting to swing state status before the Civil Rights Act).
In 1957, Lyndon Johnson was one of 3 of the 22 ex-Confederate State Senators to refuse to sign the Southern Manifesto, the pledge to resist integration at all costs. He was joined by Ralph Yarborough (also of Texas) and Estes Kefauver of Tennessee. Yarborough is a good example of what the "left" of Southern politics could look like. He was a committed New Dealer Democrat in the model of Sam Rayburn (another Texan and Speaker of the House during much of Roosevelt's Administration), a committed liberal, and voted for every piece of 1960s Civil Rights legislation, famously beating George H. W. Bush in his Senate Reelection bid in 1964 despitte Yarborough having just come off of voting for the Civil Rights Act of 1964 a few months prior. Yarborough eventually lost his 1970 primary to a much more conservative Democrat named Lloyd Bentsen, who held that Senate seat for decades afterwards.
Who were the conservatives in Texas opposed to people like Yarborough? Certainly, a few of them, especially later on, were Republicans like the aforementioned John Tower, who in 1964 was the only Southern Republican Senator and of course voted against the Civil Rights Act. Most, however, were Democrats. Allan Shivers, governor of Texas from 1949-1957, was an ardent hardliner Jim Crow Segregationist and hard line on other right wing issues (he advocated making joining the Communist Party a death penalty offense) and prominently endorsed Eisenhower over his own party's Presidential nominee Adlai Stevenson. Later, one could point to John Connally, also a Texas governor 1963-1969, who was loyal to the party through the 1950s and 1960s, but always deeply conservative. In 1972, Connally would found "Democrats for Nixon" and in 1973 he'd join the GOP. (Connally would later blow 10 million dollars of his own money on a doomed bid for the 1980 GOP Presidential nomination which went absolutely nowhere, but that's a different story)
So, who's the real Texas Democrat in 1960? Yarborough or Connally/Shivers? The answer is they both were. Until the rise of the GOP, if you wanted to get anywhere in Texas politics, you ran as a Democrat. Pro segregation? Anti segregation? Pro New Deal? Anti New Deal? Democrat. This pattern only starts to get broken when John Tower broke through in 1961, and by the 1970s, the GOP in general was totally competitive with the Democrats, with Texas electing its first Republican governor since Reconstruction, oil tycoon Bill Clements, in 1978. 1976 would be the last time Texas would vote for a Democrat for President, Jimmy Carter. By 1998, the GOP controlled every statewide office in Texas and hasn't lost a single statewide election since, and by 2002 the GOP picked up the Texas State Legislature and hasn't let go of that since either.