Well, the Egyptians used to believe baboons worshiped the Moon because they howled at its rising; that's why the god Thoth, who was a Moon god, is often depicted as a baboon. Makes sense that if any animal has religion the way we do, it's going to be a primate; their social hierarchies are so similar to what most organized religions involve!
As far as disorganized religion goes, my cat is definitely a Zen master.
Intuitively, I'm inclined to agree with Rainer Maria Rilke - who is, I think, trying to say that the animals are, even without formal religion, connected to God in a way our 'civilised' humanity prevents us from being, but he says it a lot better than I could:
With all their eyes at once the creatures gaze
Into the Open, but our eyes are turned back
And set like blind white traps to catch
Tree, animal and child before they know they're free.
Only from the dark animal gaze do we really know
What's out there, since we snatch the young child
And wrench it round so all it sees is objects and not
Subjects, and never the Open which is the deepness
In animals' faces. Only we can see death; the free
Animal has God in front and death a long
Way behind, so when it moves, like a fountain
Already in eternity it moves, a fountain.
(from The Duino Elegies)
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"Grunge? Isn't that some gross shade of greenish orange?"