Question

Why did JFK lose popularity for supporting civil rights?

Answer 1

Well because people didnt really get the "ALL MEN ARE EQUAL" quote and they didnt think all men were equal so they lost interest 

Answer 2

Many white Southerns, Dixiecrats, and conservative Republicans did not support Civil Rights, so did not want Kennedy to create laws concerning Civil Rights because they would give blacks more power and therefore Kennedy did not have a mandate and could not pass much legislation.
hope this works :)