Two hypotheses:
1. The Democratic Party in NY was less Catholic-dominated than in cities such as Boston and Chicago (ie large number of Jews and Manhattan liberals), so perhaps they felt it was less ''their'' party
2. The Catholic Church leadership was particularly conservative in NY
In NYC in the 1930's and 1940's, if you were a working-class Catholic, you were either a pro-New Deal Democrat or a pro-New Deal liberal Republican like Fiorello La Guardia. After La Guardia left office, a lot of non-Irish Catholics felt left out of the Democratic party machine, and voted GOP. A lot of Jews did, too; Jacob Javits - more liberal than even most NYC Democrats - cited the Democratic Party's corruption as the main reason he became a Republican.
