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.
Immigration was not an issue at all in 1960. Kennedy was thought to be a strong anti-communist. Bobby had worked for Joe McCarthy.Even the unions, at least the Catholics in the unions were known to be strongly anti-communist. One of JFK’s loudest complaints was about the “missle gap” between the USA and the USSR. And as for the Houston speech, it was aimed as much at the liberal Protestants, such as Oxnam, the head of the Methodists as at more fundamentalist Southern Protestants. Religion was a big, big issue. Kennedy won a big round when he took the West Virginia primary, where ole Joe bought off a lot of local democratic officials. West Virginia was strongly protestant, and Hubert was angered because he knew this neutralized the religious issue.