Going by the Catholic Church's track record (like thinking Franco was the greatest), it's safe to say this has more to do with his expansion of birth control, pro-gay marriage stance and staunch anti-Catholicism than the actually terrible things he's doing.
(I'm not the one who reflexively supports the church, and they paid a big price for embedding themselves in the political and social establishment, but...)
...maybe the church is really alarmed by his death squads? The same way they helped topple the proto-fascist Marcos regime? And that his pro-birth control, pro-SSM, and ramblings about how the bishops are all "full of sh*t" is the same trolling he used against the Obama administration?