Religion is, as you might guess, a *very* touchy subject. Here and there, some writers will nibble aorund the edges, but, as Torg taught us, you have to be CAREFUL with this stuff. Few things are as personal as someone's private beliefs.
As for myself, I'd like to see a tad more religion in-game, or at least a few more believers. When times are rough (And, in Shadowrun, times are tough more often than not!), people find some strength through their beliefs. Doesn't matter if it's Yahweh or Grandfather Coyote or Odin or 1000101, whatever someone chooses to believe in, and invoke, should come through. Havng a handful of 'runners that fire off a quick prayer or an 'Our Father' before taking a big risk, or leaving a small sacrifice to the sky father, whatever, in the middle of all the usual grim-faced types is a nice change.
For teh Shadowrun game world, the Catholic Church got kicked out of several places and had a Pope who kinda scuttled relationships badly, but has been slowly working to repair things. The Church has been active in Aztlan since the 40's, trying to get back what they lost and drive out the blood magicians, for instance, while in Europe, they battle against vampires and the Black Lodge. (Or were infiltrated by the Black Lodge, depending on who you believe.)
Making a VALUE judgement on these organizations ia a bad idea, but, as long as you're respectful, you can use them for in-game plots, I think.
Just, please, for the sake of everyone, walk carefully.