There are at least two reasons why some people will not accept change.
First, some changes can go against specific beliefs that people hold. For example, many people believed (and still believe) in the importance of sexual chastity. They believe that it is wrong to have sex outside of marriage, for example. Some of the changes in the '60s would have gone against that specific belief and would therefore have been unacceptable to those people.
Second, some people are simply resistant to change because they are comfortable with the way things have been. It is not that they are particularly dedicated to the idea of segregation or of women being confined to a certain place in society. Instead, they are simply inclined to stick with tradition for tradition's sake.
Both of these were reasons why some people didn't accept the changes of the 1960s.