An argument can be valid and still used for legal cultural subversion. The argument was that blacks are American citizens under the law, and the state cannot treat one person different than another based on race. They argued that White facilities and neighborhoods got better support from the government, directly or indirectly.

I do not see why "no segregation" has to mean "forced integration". The Civil Rights act being forced on private businesses is to blame. If we had freedom of association, people would naturally segregate.