Though the Conservative movement began to build in the 1950s and reached a crescendo of sorts with the Republican nomination of Barry Goldwater for President in 1964, some historians contend that The New Right movement did not really emerge until the late 1970s, arguably around 1976. It is important to remember that Goldwater lost the 1964 election to President Lyndon B. Johnson in a landslide.
In their book, Chain Reaction: The Impact of Race, Rights, and Taxes on American Politics, Mary and Thomas B. Edsall argue that the emergence of The New Right, or The Silent Majority, can be linked to the issues mentioned in their title. The Silent Majority was mostly composed of older, white Americans. As the previous educator mentioned, many of them lived in The Sun Belt. Goldwater was, after all, a senator from Arizona.
The Edsalls provide the three reasons that you seek in your question. They contend that the instability caused by race riots encouraged whites to seek politicians who were more authoritarian, which partly explains the election of Richard Nixon in 1968. The adoption of affirmative action policies in the 1970s diminished white privilege and supremacy.
In 1976, the Hyde Amendment, a bill introduced by Illinois Representative Henry Hyde, disallowed government funding for abortions. This was the first legislative response to the 1973 Supreme Court decision Roe v. Wade. It would lead to other efforts to limit, or discourage, women's access to abortion. Abortion, by the late-1970s, had become the issue that would mobilize evangelical voters.
In regard to taxes, the Edsalls explain the appeal of conservatism to white, blue-collar males. Economically, the 1970s was a difficult decade impacted by inflation. Furthermore, wages stagnated, while the tax burden increased. The perception was that tax dollars were funding welfare programs that catered mostly to blacks, Latinos, and the waves of immigrants who were still arriving in major cities.
Lingering racism and ambivalence about the changes wrought by the Civil Rights and women's rights movements created insecurity among many older voters and white male voters, particularly those of the working-class who worried for their jobs and their modest possessions.
This confluence of events set the stage for the election of Ronald Reagan, who promised to cut taxes. He appealed to some voters' nostalgia for the post-war era, in 1980.