Senator John Kennedy did not have a strong record on the issue of civil rights. His vote against the Civil Rights Act of 1957 exemplified the degree to which he appeared to place his political future, with presidential ambitions, ahead of broader considerations regarding the future of race relations in this country. Given his own efforts at overcoming ethnic and religious prejudices in his campaign for the White House -- his Irish Catholic background concerned many Protestant voters -- his lack of vocal support for the cause of African-American civil rights has lead to speculation regarding his motives.
By the time he was elected President, the issue of racial discrimination was assuming greater visibility. The 1960 report by the Civil Rights Commission provided quantifiable evidence that the depths of that discrimination went deeper than many whites may have wanted to acknowledge. Whether that data influenced John Kennedy is uncertain; it very likely influenced his Attorney General of the United States, his brother Robert. To the extent the new Attorney General was able to affect the president's policies, and it is well-known that the two brothers were very close and that the president sought his younger brother's advice on a regular basis, it is unlikely that the portrait of race in the United States depicted by the Commission report did not influence the president's thinking.
Another major development that would have compelled President Kennedy to adopt a more forward-leaning approach to civil rights was the lawsuit filed by James Meredith, an African-American military veteran denied admission to the University of Mississippi. Meredith's case ultimately made its way to the U.S. Supreme Court, which found in his favor. White opposition to Meredith's attempt to enroll at the university degenerated into violence, during which the federal marshals that Attorney General Kennedy dispatched to enforce the court order were physically attacked and many were injured. The attack on the federal marshals could not be ignored or downplayed by the White House, which responded by sending federal troops to the university.
Next, televised images of African-Americans being brutally attacked in Alabama in May 1963, at the behest of Birmingham Commissioner of Public Safety Eugene "Bull" Connor, a virulent racist who had publicly opposed desegregation, deeply affected many Americans, probably including the president. Finally, the 1963 March on Washington placed President Kennedy in the position of having to be more forceful in advancing the cause of civil rights.
President Kennedy's record on civil rights appears to have been greatly influenced by domestic political considerations. It could be argued that events conspired against any inclination he may have had about downplaying the issue of racial segregation.
JFK wanted to assure his presidency over Nixon before the attempt to mess with such a sensitive issue. So much so, he had opposed Eisenhower's Civil Rights Act of 1957. But he first began to take the side of civil rights when James Meredith had applied to the University of Mississippi (an all-white college) in order to get his doctorate. Meredith was turned down, which, in turn, he had sued the school because of the discrimination before him. You must understand, also, Meredith had gained growing support because he had previously served in the military for 10 years---and now he's being rejected just because of his skin color?