Final answer:
Justice John Marshall Harlan was the sole dissenter in the Supreme Court's majority decision in Plessy v. Ferguson, which upheld 'separate but equal' segregation laws.
Step-by-step explanation:
The person who disagreed and denied Plessy's request for a writ of prohibition in the Plessy v. Ferguson case was Justice John Marshall Harlan, who was the only Supreme Court Justice to dissent from the majority opinion. Justice John Marshall Harlan was the sole dissenter in the Supreme Court's majority decision in Plessy v. Ferguson, which upheld 'separate but equal' segregation laws.
The majority of the Supreme Court upheld the constitutionality of Louisiana's segregation law by a decision of 7-1, establishing the doctrine of "separate but equal". This ruling affirmed the legality of racial segregation as long as the separate facilities provided for each race were purportedly equal in quality. The decision stood as legal doctrine until it was overturned by the landmark case of Brown v. Board of Education in 1954.