Starting in the late 1990s, they have asked about "a generally well-qualified person who happened to be Jewish"--over 90% have said that they would. In the late 1950s, the percent saying that they would vote for a Catholic was only a little higher than the percent saying they would vote for a Jew. Since Catholics were about 25% of the population and Jews were about 3%, that suggests that among Protestants, willingness to vote for a Catholic was lower than willingness to vote for a Jew.
In April 1960, the Gallup poll had a survey asking about hypothetical contests for President, including Kennedy vs. Nixon. In that match, 46% said they would vote for Kennedy and 44% said Nixon. Then they asked "As you may know, Kennedy is a Catholic in his religion. Supposing Kennedy were NOT a Catholic—which man would you like to see win—Nixon or Kennedy?" 51% said Kennedy and 40% said Nixon. In October 1960, they asked "AS YOU KNOW, SENATOR KENNEDY IS A CATHOLIC. HAS THIS FACT MADE YOU MORE IN FAVOR OF HIM, LESS IN FAVOR OF HIM, OR HASN'T IT MADE ANY DIFFERENCE AT ALL? (Oct 1960)" 5% said more in favor and 19% said less in favor. That is, Catholicism made a difference to voters in 1960, and it didn't take subtle techniques to detect it.
Starting in the late 1950s, Gallup also asked about voting for an atheist:
Willingness has grown, and it's now a little below willingness to vote for a Catholic or a Jew in the late 1950s. I also show two from Time/CNN/Yankelovich surveys in the 1990s, which asked "Would you vote for a candidate for President who did not believe in God?" Those showed much lower support, although by a dictionary definition "did not believe in God" is weaker than "atheist," since it could be interpreted to include agnostics. Unfortunately, those questions have not been repeated.
In 2003, the question was asked about a Muslim for the first time--56% said they would. In 2012, it was 58% and in 2015 it was 60%. Given the short span of time and the sample sizes, it's hard to say if that's an upward trend. In 2015, a Suffolk University/USA Today poll asked "Would you vote for a qualified Muslim for president?": 49% said they would, 40% said they would not.
[Date from the Roper Center for Public Opinion Research]