This specific exception would obviously not have made any sense back then, considering the vast majority of refugees belonged to the minority religion.

I actually just tried to find out what the attitude towards jewish refugees was in the US and happened upon this eerily pertinent passage:

    Out of fear that the Nazis could smuggle spies and
    saboteurs in with refugees, immigration officials
    tightened visa policies for immigrants and non-
    immigrants. The State Department urged its diplomatic
    consuls in Europe to screen potential immigrants
    carefully, including those fleeing persecution,

(from https://www.ushmm.org/wlc/en/article.php?ModuleId=10007094)

And interestingly, Germans that were at that time not even considering to migrate to the US (Werner von Braun anyone?) were just forced...