Umm - there is a difference in the way rubber & poly bushes work - at least, there is in coil spring setups, I don't have that much experience with leaf springs.
Rubber bushes are designed to flex - poly bushes are not.
Let's go withe coil springs because thats what I know best.
The rubber bushes in a coil spring suspension will usually have inner & outer metal sleeves bonded to the rubber - the outer sleeve will be a "press fit" in the control arm or link, and the inner sleeve will be clamped "end wise" - the rubber itself will flex or distort to allow limited rotational movement of the arm or link.
Poly bushes in the same setup do not flex - they are not bonded to the sleeves and will pivot typically on the inner sleeve like a bearing and this is where the squeak comes from.
In a leaf spring suspension - one end will mount to the chassis, and the other has the shackle(s) - the chassis end has very little movement and the rubber is for isolation. The shackle end however moves back & forth as the suspension flexes and you will probably see the same pivoting action that I describe above, and get the same squeak.
I've never put poly bushes on a leaf sprung vehicle, I have put them on a coil sprung street car - they make for a very firm ride, awesome road holding, and if not properly lubed - a very annoying squeak.