Many evangelicals hated JFK not for his Catholicism but for being soft on Communism, pro-Third World, pro-union and a welfare-state socialist.
True, JFK was a pro-immigration lefty, and Protestants, who had only voted Democrat twice in history, voted for JFK in about the same numbers Democrats had gotten in recent elections.
JFK got 43% of the Protestant vote which was better than the 42% of 1952 and 1956.