I use Weldwood contact cement extensively.

Can't say I've glued leather to rubber, but I have glued leather to wood (two absorbent materials) and wood to rubber (one absorbent/one non-absorbent).

I make sanding blocks by gluing hard rubber gasket material to strips of hard maple, then cutting them with a chop saw. Not only do they survive the saw, some I've used for 20 years and never had one delaminate.