We all know rubber is known to have a high friction coefficient, and it's quite difficult to drag a block of it across a surface. What happens when two blocks of flexible rubber are dragged against each other, and by how much does polishing the surface of rubber affect it's friction against another polished rubber surface?
Rock climbing shoes are made with rubber that is formulated to be as sticky as possible. Steven Won has done tabletop experiments using climbing shoes on the rough back side of a granite slab from a kitchen countertop, and has estimated $\mu_s=1.17$. I did a quick and dirty experiment just now by putting a climbing shoe on top of an upside-down climbing shoe, so that the soles were in contact. I tilted them until they slipped. My result was about $\mu_s=0.99\pm 0.05$. So it appears that rubber on rubber does not have a higher coefficient of static friction than rubber on granite.
by how much does polishing the surface of rubber affect it's friction against another polished rubber surface?
I don't think you can really polish rubber in the same sense that you can polish materials like metal or rock, and I don't think the frictional properties of rubber depend very much on the details of the shape of the surface. That's why road bikes tires and rock climbing shoes have no tread pattern.