The UN has historically been supported by the Catholic Church in its mission to help maintain peace and commerce in the world. Far, far further back than this, the Church has consistently been a “pro order” institution. Early Christians prayed for the very emperors who decreed their persecution, torture, and death. When the Roman world fell, Christians showed much sympathy, even in spite of its decadence and inconsistency in obeying the gospel.
The fearful side to this today (and has always been in the past), is that you can use large government bodies to try to maintain peace & prosperity, and ultimately be a channel through which the Church can evangelize (it’s hard to do this when there’s anarchy, isolation, and war), but… what happens when these governments do the complete opposite? What if you’re just setting yourself up for disaster?
I’m not sure that there is an easy way to answer this. You support unity, and then you try as hard as you can to keep that from happening.