2 days
that also seems anecdotal… I personally never heard of a single one (oh, anecdotal too) and in all cities I’ve lived I knew of shelters and rescuers because I’m one (and I currently take care of 34 cats and 4 dogs), and I must agree with OP, I know a lot of rescuers that have a religion (like, that vague belief in the god their parents talked about) but none that are overtly religious (wear symbols, attend temples, etc)
edit: Homeless shelters and nursing homes though, plenty of religious institutions behind them.
I mean, MAD magazine been doing those since the 50s… as for movies, you mentioned some 90s stuff, in the 90s we also had Blankman, Mystery Men, Meteor Man…