I knew a person who had a cat with a religion of 'up'. Specifically, the trapdoor in the ceiling which led to the attic. Every so often one of the humans would open it and go up there, and when they did things either appeared or disappeared. When the cat was upset (like when one of their other animals died) the cat would go and sit under the trapdoor and look up at it and mew, obviously expecting or hoping that their companion would come back from there like other things had.

As you say, their beliefs tend to be based on past experience, but then so often are ours. Many 'superstitions' are actually based on experience -- after you've had a bad thing happen just after seeing a black cat enough times it becomes natural to connect the two. And walking under ladders is just a bad idea in general, especially when there's someone up there wit a paint pot. For that matter enough people have direct personal experience of things like prayers being answered to convince them, even though there is no way that they can 'prove' it to anyone else. If you do a dance and it then rains, several times (even if sometimes it doesn't rain), you're likely to do that dance every time you want rain just to improve the odds a bit...