Was America’s shift to the political right “conservatism,” i.e., “saving” or “holding on to” gains, or was it a “reaction” to the numerous and sometimes violent changes of the Sixties?
During the period from 1969 to 1988.
It is best to characterize this period in US history as a reaction to the changes of the 1960s.
During the 1960s, the United States moved toward the political right in many ways. The government started to spend much more money due to President Johnson's "Great Society." It started to do more regulating of the economy because of things like the environmental movement. American society was being pushed away from traditional values by such things as the counterculture that sprang up in the 1960s.
All of these things led to a serious backlash. Many Americans (in President Nixon's terms, the "Silent Majority") were very concerned about these changes. They felt that the United States had moved too far away from its traditional values and attitudes. This led to the swing back to the right that can be said to have started with Nixon's presidency, but which really took off with the "Reagan Revolution."