The right answer is the A: The Warren Court believed that segregation did in fact stamp African Americans with a badge of inferiority.
In the 1896 Supreme Court case Plessy v. Ferguson the legality of racially segregated public facilities (i.e. separate facilities for blacks and whites) was restated, as long as those facilities were equal. All the judges, with the exception of one, rejected Homer Plessy’s (the plaintiff) argument that having cars in trains specifically for “colored” passengers was unconstitutional, and deemed it fallacious his belief that those segregated cars made blacks look inferior – this is illustrated in the extract from their ruling that is included in your question. This idea of “separate but equal” was upheld for decades, but in 1954, another landmark case, Brown v. Board of Education of Topeka, questioned it, and the Warren Court, led by Chief Justice Earl Warren, ruled that segregated facilities, specifically public schools, were indeed unequal, and, therefore, unconstitutional, and their existence contributed to perpetuate the false, yet powerful and harmful, belief that black people were inferior.