Without reading between the lines I’m pretty sure my 1937 Sunday Missal rails against the New Deal with its frequent calls for true “Catholic Action” in the end pages. They seemed to know then that an expansionist state was bad for the church and the faithful.
Unfortunately the Catholic community "took advantage" of government dollars and paid a price. They had to adhere to secular government regulations. Illinois Catholic Charities would still be in the adoption business if the church would have looked to the Lord for their provision.
If the Catholic church was teaching that during the New Deal, it wasn't learned by Catholic voters, they were part of Roosevelt's, and then the Democrats, New Deal interest groups.
"The New Deal Coalition was the alignment of interest groups and voting blocs that supported the New Deal and voted for Democratic presidential candidates from 1932 until the late 1960s. It made the Democratic Party the majority party during that period, losing only to Dwight D. Eisenhower in 1952 and 1956."
Three of the three times that the democrats have won the Protestant vote were during that New Deal range, but that was narrow support for FDR in 1932 and 1936, then they saw the light again and voted against FDR in 1940 and 1944 and in every other presidential election except for 1964.