Though I have developed a more mature approach since starting this thread, and it's embarrassing to me to see how crazed I used to be, saying Montini is a Jew is apparently proven. Father Saenz y Arriaga and others state flat-out he had Jєωιѕн ancestry. Famously, he wore the Jєωιѕн breastplate, the ephod.
Even if there were no direct proof, it would not be wrong to suspect him of being a Jew, because his actions lead directly to that suspicion. Suspicion is only wrong if there isn't sufficient basis for it. Some people adopt the pseudo-pious position that this means we must have proof, preferably a video or a photograph or whatever. But if we had that, it wouldn't be "suspicion" anymore, would it? Suspecting someone of being a Jew because they have a big nose and are cheap would be wrong, but it is not wrong to suspect the "Pope" who convoked an anti-Catholic and Judaizing Council, who wore an ephod, and who spurned almost every element of the papacy -- going so far as to be buried in a plain wooden coffin -- of being a Jew.
However, that is all moot since apparently it is proven that Montini's mother is a Jew. That makes him a Jew. Period.