They say that Russia was comprised of only 2% Jєωs before 1917, and after the Communists took over that country, the Jєωs comprised 80% of the new Soviet Socialist Republic.
My point being, it doesn't take much infiltration to cause a big problem. Judas Iscariot was one man.
The problem we are having today was allowed by Christ as punishment, and He previously sent Our Lady of the Rosary at Fatima to tell us what the preventative/solution would be.
The Freemasons and modernists were a very small part, but they took the clergy off-balance just enough so when the clergy were faced with a massive nuclear1 threat against Rome and perhaps the families of the Cardinals, it was enough to throw things into confusion, and the wrong people to gain control.
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1 I have good reason to believe