Hitler had to kill Catholic priests because they wouldn’t knuckle under; the popes (Pius XI & Pius XII) were openly critical of National Socialism, and had the German clergy read pronouncements to that effect.
In Italy, in return for recognition of the Italian state, the Church was given a role in public education. That probably plays no small role in why the Italians never targeted Jews (though the Germans did after Mussolini was deposed, and they were basically occupying Italy).
Apparently all but the rabid liberal Catholics (ie nancy pelosi) are really ticked off.