Remember the views of the time - in the 1950s the Democrats were the party of Strom Thurmond & Segregation, and it was a Republican President (Eisenhower) who sent Paratroopers and US Marshalls in to enforce school desegregation. Many of the things you view as Liberal were not seen as such as the time, indeed they were more heavily featured in the Republican platform than the Democrat one. That all changed with JFK, LBJ and Nixon - but Warren was appointed before that, and is really not all that inconsistent with the values of the Republican Party & President who appointed him.
The Democrats were not the party of Southern Segregation since the 19th century. In the 1950s, the Democratic party was the very divided but under one banner party of the Northern Democrats and the Southern Democrats. So much so, and so recognized as so, that the distinction of votes in congress in the journal of record on that issue was measured and noted as ND, SD and R (Northern Democrat, Southern Democrat and Republican). Those things were very much seen as Liberal at the time. Precisely why they factored into the platform of a Republican party dominated primarily by the Eastern Establishment -- Liberal and Moderate Republicans. This all came in what was named the "Liberal Consensus": the Post-War, Post-New Deal era where Hoover and the rest of the laissez faire had been debunked, in the opinions of the time. And the consensus was that everything of the New Deal was here to stay in terms of societal and government infrastructure. Eisenhower himself was a moderate. Eisenhower himself noted "Should any political party attempt to abolish social security, unemployment insurance and eliminate labor laws and farm programs, you would not hear of that party again in our political history." This was precisely in reaction to Conservatism, as the divisions, differences and existence of Liberalism and Conservatism were there and understood to be there. It is simply a matter that the Liberals won, had the majority, and Conservatism was an oddity for regions of the country that could not overwhelm the Liberal Consensus. That being said, the Conservative Coalition of Southern Democrats and Republicans did exist as well, and prevented any major move forward in terms new of social liberal programs until 1964.
These things were exactly viewed as Liberal at the time. Or at least certainly anti-Conservative. Barry Goldwater was in favor of racial equality, indeed being a member of the NAACP. But Goldwater absolutely opposed the Civil Rights Act and government intervention into Civil Rights on the basis of "big government" opposition. You could see similar statements from some urbane, higher minded Conservatives. Many of his Conservative fellows were not so well intentioned. At best, you might see something like Black Americans were children, who were not prepared for racial equality, but bless their hearts. Many White Americans had this view. Just a little ways down, you had the opinions of Southern Democrats, and Conservatives coming out of the quarters of the John Birch Society or having a similar hate filled view to said group (many of them supporting Goldwater, by the way) who viewed Black Americans with an absolute disdain, thought they were dangerous, refused to accept them in their society, thought Martin Luther King was a Communist agent, and viewed government action forcing Black equality with them as a slap in the face. And if JFK got shot, good for the assassin. You literally have so many stories where in Southern schools and stores and restaurants, people applauded the news of the Kennedy assassination.
So, in brief summary, that statement is absolutely incorrect. The logical fallacy is to assume the Republicans of that era were Conservative, and therefore those actions approved by the court were not viewed as Liberal or anti-Conservative. The fact is that the Republican party of today was not the Republican party of that era. The Republican party of that era was divided between the Liberals/Moderates and Conservatives. They were once headed by Thomas Dewey and Robert Taft, respectably. They were later lead by Nelson Rockefeller and Barry Goldwater, respectably. Indeed, Eisenhower was put into the running precisely to stop Taft from getting the nomination: a moderate that Thomas Dewey backed over a Conservative that Taft was. Goldwater's movement in 1964, in conjunction with the changes, issues and divisions of the 1960s, placed the Conservatives in a stronger position which they would eventually use, over the course of the 1970s, to make the Republican party a Conservative party as had been seen in the 1930s. Establishment Republicans were kicked out of the party, never to have any presence on the national stage of the party again. When asked in the 1970s where the Eastern Establishment was, Nelson Rockefeller replied, whether a direct quote or a paraphrase, "You're looking at him" because they had so severely dwindled. Many of them joined the Democratic party. Many of them existed in some degree on the local and state level in receding regions of strength in the north. For their party, the Democratic party had long been divided by starkly different factions, north and south, totally at odds with one another, often fighting and undercutting one another, and totally separate parties under one national banner. With the rise of Goldwater and the Conservative conquest (to name it that) of the Republican party, the Southern Democrats would become Republicans precisely on the basis of Conservatism inspired by complete opposition to government enforcement of racial equality and integration. It is more complex than that, but the complexity does not undercut, let alone debunk, that fact. Southern Democrats could be Liberal on anything but Civil Rights. The government could build bridges and schools and enforce stronger wages and do a lot. There were factions of Southern Democrats as well, but they were generally unified on opposition to Black Americans having any place but hate and expulsion among them, and as Civil Rights proceeded, even Southern Democrats with some support for anything Liberal went Conservative on everything.
Conservatism and Liberalism were understood in that era, and clearly defined. The only deviation would be a discussion on the New Dealers versus the New Left, which that is a difference on definitions of Liberalism (Vietnam, drugs, etc. Whether certain opinions and policy concerning them are Liberal or not.) And we are not even dealing with that in terms of this discussion between this post and the quoted post. Conservatives and Segregationists hated Earl Warren because they viewed him as a (Yankee) Liberal, because he legally supported federal intervention in local and state matters. They ran a campaign that he should be impeached. And I will end on this image.