Final answer:
The rationale in Plessy v. Ferguson established 'separate but equal,' leading to legally sanctioned segregation and inequality until overturned by Brown v. Board of Education.
Step-by-step explanation:
The Supreme Court's decision in Plessy v. Ferguson (1896) had a significant impact on American society. The Court's ruling established the doctrine of "separate but equal," which upheld the constitutionality of racial segregation under the premise that the separated facilities were equal. However, in reality, this legal doctrine legitimized state laws establishing segregation and resulted in the inequality of public facilities, maintaining racial discrimination and the marginalization of African Americans until it was overturned by Brown v. Board of Education in 1954.