Continuing my exploration, I found a 1958 Gallup Poll that asked "Are people who are intellectual more likely to be Democrats or Republicans?" The most popular answer was "no opinion," at 39%, followed by "Neither," at 27%. Only 15% said Democrats, and 19% said Republicans. This question was asked after the Democrats had nominated Adlai Stevenson, who had a reputation as an intellectual, for president in both 1952 and 1956. Apparently the identification of intellectuals with Democrats hadn't caught on in the general public.
The survey also asked "If you were going to a meeting of the garden committee of the Women's Club, would you find more Republicans or Democrats there?" Again, the most popular answer was "no opinion" (50%). 24% said Republicans, 12% said Democrats, and 13% said "neither." People had a stronger impression in this case, but it still wasn't very strong.
It would be interesting to ask similar questions today. People who are interested in politics are constantly offering generalizations (or stereotypes) about the tastes, lifestyles, and occupations of Democrats and Republicans, but it's hard to say how much of this has sunk in with the average person.