With specific reference to racial laws, the Constitution and the 14th Amendment has been repeatedly interpreted as prohibiting discriminatory laws. That's not so much the problem anymore as much as laws that are not intended to discriminate, but end up having that effect. "Color blind" is an absolute that doesn't exist either in society or in government, but it is the ideal we pursue. How about a school funding system based on property values that tends to create sub-standard schools for minorities with a higher urban population and a higher tendency to be poor. While not the intent of the law, that may well be its effect.
I will argue that it does not. The 14th Amendment does say that all people have to get the equal protection of the laws. But this is clearly only meant to mean "within reason." For example, you could argue that allowing segregated bathrooms for men and women does not treat everyone equally, right? The same goes for race. If there is a good reason to treat the races differently (for example, to make up for past discrimination) I would argue that the Constitution does not prohibit this any more than it prohibits single sex bathrooms or banning women from participating in combat.