“The Vatican” has a lot of scandalous dissenters in it (for a hierarchical church with all the prerogatives that implies, I think the Roman Catholic church is not using its power very wisely — but I caveat my bias as an unabashed evangelical or as some put it “Protestant”). I can’t imagine the present pope taking a radical anti-private-arms stance though he may preach for general peace.
You sound like Russians who used to say if Comrade Stalin only knew what was going on he would surely stop it, even as they were sent to the Gulag. Face it, the church is liberal on most issues like immigration, redistribution of wealth, and now guns.