faith auto purchase and puppets

Will puppets purchase faith buildings? If not, religious centers+feed the world looks much more appealing to me.

nope, they do not purchase buildings with faith (Cathedrals/monasteries/Mosques/Pagodas). That would be OP (same thing as puppets buying units).

Puppets BUILD shrines and temples though, which is what you're referring to with those beliefs.

Thanks, good to know. Religious centers it is.