Was the Civil Rights Amendment Good or Bad? What was the purpose?
It would be opposed not necessarily for the effects it wants to lead to–inclusion for all people regardless of status and extension of legal rights to them–but for its effect on the relation between state governments and the federal one. The Civil Rights Amendments essentially extended the same protections our federal government provides to people to the state governments, which subverted some of their Constitutions and laws. If you are an advocate of state sovereignty and someone who opposes a large federal government, you would certainly oppose anything that imposed a new requirement on states, when the states are supposed to be able to set their own policies and pass their own laws that are immune to federal interference.
