Southern whites were probably worried that the federal government would try to change their way of life during this era. The Reconstruction era was focused on uniting the US after the bloody Civil War. This task, however, proved to be very worrisome for whites in the South. This was due to the amount of constitutional changes made during this period.
The 14th and 15th amendment helped to give former slaves rights like citizenship and voting rights. This probably worried whites, as now African-Americans had the ability to change society by being involved in the political process. However, the southern states will find loopholes to continue to prevent African-Americans from enjoying these rights guaranteed by the US Constitution.