Two things happened in the 60s and early 70s: the Goldwater faction largely took power in the Republican Party, and because the Democratic Party embraced civil rights, the Dixiecrats first flirted with independence (George Wallace's campaign) and then gradually switched parties, so now we have the oddity that there are people who fly Confederate flags but are registered members of the party of Lincoln. Many people who would have been Republicans in the old days are now the moderate/neoliberal faction in the Democratic Party.
So we still have four parties, they were just reshuffled. Now the tension in the Democratic Party is between the old FDR/LBJ new deal supporters, and their younger socialist allies, and the more pro-business neoliberals. On the Republican side it's between the business side (they don't care much about ideology, they just want to make money) and the hard-core conservatives.
No, I'm saying that the description that polarization was absent is wrong.
I'm also saying alignment of the axis of differentiation between the major parties in a two-party system and the salient divides in society makes it easier for people to make meaningful choices, and feel they are doing so, by voting.
When there are sharp polarizing social/political divides, as there were over many issues in the 1950s, and they are not reflected in the divides between the parties (as they often weren't in the 1950s), then the government cannot represent the people because the people cannot express their preferences on important issues by voting.
There was not a lack of polarization and divisiveness in American society.
The divides in American society and politics didn't map well to the two major political parties because there was a major political realignment in progress and the parties hadn't yet aligned with the divides in society.
The problem was the divide between the major parties not being sharp on the issues where there were, in fact, sharp, polarizing divides in society, preventing members of the public from effectuating their preferences on salient issues by voting.