Remember the original PotA movies, where Milo, Cornelius, and Zira salvaged Taylor's ship and flew back in time to 1970s Earth?
The same thing happened here. Ape Lincoln was Thade. He salvaged Walberg's crashed ship from the swamp, and flew back in time to lead an ape revolution.
At least, that's the only thing I could come up with that would explain it.
Forced perspective. It's impaled on the pitchfork, which is being held toward the camera. The person in the background is at least 3 feet farther back, possibly more. The camera is also quite close to the rat. Both of these make the rat look much larger than it really is.
They can be considered a cult, as they have a doctrine that is regarded as absolute truth and not to be questioned, delivered by a leader whose word is considered final and absolute, also not to be questioned.
Here's an essay from Skeptic magazine "The Unlikeliest Cult": [www.2think.org]