What led to the conservative (political and cultural) resurgence from the 1970s to the present and what is the lasting legacy of the shift to the right? How important was the shift, and what parts of the 1960s did society manage to hold on to, despite the conservative resurgence? How has this shift to the right transformed domestic and foreign policy today? What is the legacy of this shift?

Several factors led to the so-called "conservative revolution" of the 1970s. One was popular unease with the pace of social change in the country, especially in the late 1960s. Many people believed that the changes set in motion by the Civil Rights Movement in particular had moved too far, too fast. Conservatives who opposed policies like affirmative action found willing allies among white Americans throughout the country.
Many Americans, especially evangelical Christians, deeply opposed some of the changes related to gender roles (including the rise of feminism), the proposed Equal Rights Amendment to the Constitution, and abortion. They resented the Supreme Court under Chief Justices Earl Warren and Warren Burger that expanded individual rights, particularly the rights of the accused.
They thought the policies of Lyndon Johnson's Great Society were socialistic and wasteful, and they deplored the disorder they saw on the streets of many urban areas, which they blamed on radical insurgents and criminals. Many were also deeply offended by what they saw as the anti-Americanism of protests against the Vietnam War, the failure of which they also perceived as an example of America's weakness abroad.
These factors, in addition to the terrible economic stagnation of the 1970s, which affected working-class Americans, contributed to a conservative backlash that brought President Ronald Reagan into office in 1980 and moved the nation firmly to conservatism, at least in government. Its main effect has been that measures that once received bipartisan support during the period of "liberal consensus" following the Second World War—some kind of universal healthcare system, for example—are now bitterly contested. Even many of the policies of President Richard Nixon, elected on the crest of a conservative wave in 1968, are considered "leftist" in modern political discourse.
https://www.history.com/topics/1970s/1970s-1