As you may have already seen, many teams are starting to shape their robots so that their bumpers assist with getting out of pins. 971 is a notable example with their octagonal frame this year, where the majority of their robot frame is angled so that they are more likely to be pinned from one of the angled parts where they can get out of instead of from the side or front where it's harder to get out of the pin.

The height of the bumper itself doesn't matter - it's the point of contact. Bumpers that contact each other more have more friction between each other. If both teams have their bumpers at the lowest possible point, then there is more friction between the bumpers. If one has their bumpers at the highest point, and another at the lowest point, there is less bumper friction and is therefore more difficult to pin solely due to bumper friction. What this also does is makes it easier for the robot with the lower bumpers to get under the bumpers of the robot with the higher bumpers, thereby lifting the pinned robot off the ground lessening their normal force (and their friction), and increasing their own normal force and friction, making their pinning strength a lot more powerful (and it's completely legal since it's not within the frame perimeter).

Bumper material definitely does play into the pin, since the coefficient of friction between two bumpers is dependent on the two materials. Teams have recently started making smooth leather bumpers to decrease this coefficient of friction and make slipping out of pins a lot easier.

A robot's center of mass will change where a robot rotates around when getting pinned, or if it will fall over when hit too hard. It is an option to put your center of mass off to one side making rotating out of pins through rotating that side a very viable option.