Allan J. Lichtman in *Prejudice and the Old Politics: The Presidential Election of 1928* notes that although some Protestant ministers denounced Al Smith for his Catholicism, one took a different tack:
"One Protestant divine, Henry C. Culbertson, even argued that the American people must reject Al Smith to protect the interests of the Catholic church. Were Smith to be elected, Culbertson reasoned, 'every fault or failure of his administration would ...be blamed on that [Catholic] Church.' Moreover, because of Smith's opposition to Prohibition, the Catholic church would be burdened with 'the tremendous odium of having shared in lowering the public standards of our nation on the question of drink.' Culbertson called for 'prominent Catholic prelates to come out... so strongly against Smith on this issue that no one will dare question the good faith and high ideals of that great church.'"
https://books.google.com/books?id=KbGiJpDk6pwC&pg=PA60
In a footnote (p. 305) Lichtman observes , "Culbertson's argument may have been strangely prophetic. If elected in 1928, Smith would probably not have ben much more successful than Hoover in combating the Depression, and surely many American would have blamed the president's subservience to the Catholic church for that disaster."
Now for Smith to win in 1928 seems almost impossible, but let's assume he somehow does so--say, some monstrous scandal involving Hoover is uncovered. (He sold Belgian girls into white slavery during the War, or something...yeah, I know, not terribly plausible...) Is Lichtman right that voters from then on will associate the Great Depression with Catholicism? I think it's more likely that it will simply confirm in their minds the notion that voting for a *Democrat* always leads to a depression (there were still plenty of people around who remembered Cleveland and the hard times of the 1890's; moreover, the depression of the early 1920's was blamed on Wilson.) But of course saying that it will lead to resentment of Democrats and to resentment of Catholics are not two mutually exclusive things, and even in, say, 1960 the Democrats may actually be more worried about the Al Smith precedent in considering whether to nominate a Catholic than they were in OTL... (After all, in OTL, some anti-Catholic Democrats who considered voting for Nixon in 1960 may have had second thoughts when they remembered what had happened when they or their parents had voted for another Quaker against a Catholic in 1928!)