What does one do if the visible head--the Pope himself--is a revolutionist and approves of the revolution?
Good question. From what I know of the Church's history there have been some very sorry Popes, and many very fine ones. During the periods when there were less-than-sterling Popes, it seems to me from what I know that the Church still held (despite the efforts of those who wanted to destroy it) and Christ's promise that the gates of Hell would not prevail was shown true - as all of His promises are.
What does one do? Pray. The one thing I keep coming across in past eras is that people prayed - a lot. And God raised up saints who helped lead the Church back on track. For all the controversies, I still believe that the gates of Hell will not prevail as Christ promised. Otherwise, what was the point of my departing the Protestant and Anglican side of the Tiber? (rhetorical qustion) The other thing, find parishes where there are non-revolutionary priests and stick with them.
One thing someone learns as Protestant and Anglican is to "church shop" - it comes down in those communities to finding a solid pastor and a good parish/local church. Seems one has to do likewise these days as a Catholic. At least I had a lot of experience in shopping around!
In the current situation? All I know to do is what Catholics have done in other eras - pray every day, find a solid priest and parish, stand on the promises of Christ, keep sticking to the tried and true (the old classics). I recall that some of the ancient writers indicated that to be in the Catholic Church one had to be in communion with the Seat of Peter.
Christ promised the gates of Hell would not prevail. The waters raging and dashing against the rocks and the wind howling like crazy is another matter.