What are the reasons why new conservatism rose to prominence in the US between 1960-1989?

If I were asked to name four reasons why conservatism rose to prominence in the time period you mention, I would list the Civil Rights Movement, the Vietnam War, the Great Society, and the Counterculture.  These can all be boiled down to one reason as well:  we can say that conservativism rose to prominence because many Americans felt that the US had moved too far towards liberalism.  All four of the factors I mentioned were part of this move to the left.

The Civil Rights Movement helped move America towards conservatism by awakening racial resentment among whites in the South.  Beginning with this movement, many whites have come to feel that liberals favor non-whites over whites.  The move towards conservatism is partly a move away from liberalism since many whites now feel that liberals are anti-white.

The Vietnam War helped move America towards conservatism because of the protests that it provoked. During the Vietnam War era, liberals were very anti-war.  Some liberals even seemed to be anti-America.  Many Americans who might once have been liberal or moderate were appalled by the attitudes of some anti-war activists.  They moved towards conservatism and its overtly patriotic attitudes.

The Great Society helped move America towards conservatism because it spent tremendous amounts of money trying to fix things that many Americans did not regard as problems.  Once the Great Society programs were enacted, the government was spending on (among other things) anti-poverty programs, on environmental protection, on consumer protection, and on the arts.  Now, the government was taking taxpayer money and spending it on things that did not seem important to many people or, at the very least, did not seem like things that the government should be responsible for.  Because of this, many Americans moved towards conservatism and its promise of smaller government and lower taxes.

Finally, the Counterculture helped move America towards conservatism because it seemed like traditional values were being completely thrown away.  Many Americans were horrified by the “sex, drugs, and rock-n-roll” focus of the hippies.  They felt that American society was turning its back on traditional morality and decency.  They gravitated towards conservatism with its greater respect for authority.

In all four of these instances, we see America becoming much more liberal in the 1960s.  As the country moved more towards the left, a backlash emerged among people who thought things had gone too far.  This backlash caused conservatism to rise to prominence during this time.