BTW: Did you see the evidence I posted, that you asked for, regarding Pope Pius IX being highly offended by the allegations?
Nowhere did he deny ever having joined the Masons. It's unclear exactly what he's denying, and the closest thing in there that he comes to denying is that the Holy See was an ally of the Masons ... which he clearly wasn't by that time.
Here's another topic ... similar to FE ... where it's clear that you have some psychological / emotional attachment to the outcome and won't look at it openly. I think it's possible that he joined the Masons and possible that Leo XIII did as well. Lots of people joined the Masons as it was, as the gentleman who made the video above indicated, the "thing to do" for people in certain social circles. What someone did or did not do as a youthful indiscretion has nothing to do with their later life.
Even if you take actual membership in the Masons off the table, there's no doubt that Pius IX was one of THE most liberal Bishops / Cardinals in the Church prior to his election and that he was a favorite of the Masonic-affiliated electors and the liberals among the Cardinals, and that he was converted by the graces of his office, in a clear demonstration of the guidance of the Holy Spirit over the Papacy ... vs. the R&R thesis that individuals who are liberal and have "messed up brains" would be allowed by the Holy Spirit to wreck the Church.