Hot take: Vietnam is what caused the modern schism of left vs. right in the US today, and the current alignment.
I don't agree.
Social issues weren't all that big a deal in the 1960s as, fortunately, support for Civil Rights was largely bipartisan. The differences over Civil Rights were ideological but, at least among the politicians, weren't ideological absolutes that couldn't be overcome. For instance, the dispute that delayed passage of the 1968 Civil Rights Fair Housing Act, had to do with the 'libertarian' issue of 'property rights.' Republican Senate Minority Leader Everett Dirksen was able to fashion a compromise on this over some Republican belief that an owner of a private home should be able to sell that home to whomever they wanted for whatever reason they wanted.
Senator Everett Dirksen also played a critical role in helping to overcome the filibuster of the 1964 Civil Rights Act and I believe he also helped fashion the compromise that led to the 1965 Voting Rights Act. Senator Dirksen is an unfortunately largely forgotten hero of the passages of the Civil Rights acts.
As an aside, the fight over the Fair Housing Act is immortalized in the 1967 Simon and Garfunkel song "Silent Night/Seven O'Clock News."
I certainly don't disagree that anti communism was a proxy for social issues in the 1950s and 1960s, however this predated American involvement in Vietnam with such things as the McCarthy Senate hearings and the House Un-American Activities Committee of the 1950s. For the public at large, the issue was known as the 'red scare' and involved whether a person was sufficiently anti communist or not.
Social issues didn't really become a major schism until 1973 with Roe V Wade and even that didn't really play out politically until the formation of the 'Moral Majority' in 1979. Unlike Trump who brought millions of people out to vote who had rarely if ever voted previously, the 'Moral Majority' did not really get many new voters out for Reagan in 1980, but what they did do was convince many people to vote on the basis of their religiosity. Previously, Baptists and other Evangelicals had been told that their religious/moral beliefs should not enter into politics.