Seeing how controversial Kennedy's Catholicism was, how important Barack Obama's blackness was to his campaign, and how many times Keith Ellison's dedication to the US is called into question because of his religion, I have a hard time believing that Goldwater had a realistic chance in a country that still logged numerous public servants as Klan members.
There wasn't really a need for LBJ to bring religion into it, when he could instead campaign on the basis of "Voting for Goldwater will end the world in nuclear fire."
The right wing groups that might have conceivably saw merit in campaigning against someone with Jewish heritage were, in any case, the people who got Goldwater the nomination. The John Birch Society could hardly campaign against their own choice.
Outside of a small fringe of extremists, it's hard to imagine a demographic, in 1964, that would have responded favorably to a political campaign attacking someone for having Jewish heritage.