Yea, probably wrong to paint western churches with a broad brush like that. town I grew up in had two homeless shelters that also operated as soup kitchens all sponsored by the Catholic Church, so although they may not open their doors and let people sleep on the pew, most of the established religious networks will be funding charitable endeavors in some other way.

I have no stake in this, not a fan of religions but seen a lot of homeless shelters, clinics, outreach programs, etc sponsored by established religions.