We can identify at least two reasons why there was so much resistance to change in the case of the freedom riders and the Civil Rights Movement in general.
First, there is the simple fact that people tend to feel that the status quo is somehow superior to other possible ways of life. People look at traditional ways and they believe that those ways are morally right simply because they are traditional. Therefore, they are reluctant to change to different ways.
Second, in the case of the South in the 1960s, there were also issues of power and revenge. The South had felt, at least since the Civil War, that the North dominated it and oppressed it. There was animosity towards the North for this reason. Resisting integration was a way of fighting back. It allowed Southerners to feel that they were fighting the fight that their ancestors had lost.
Thus, there was resistance to the freedom riders both for general reasons that are common to all societies and for reasons more specific to the South at that time.