Interestingly, most cheeses that don't use rennet are soft, but some of the hardest of all cheeses are the Mongolian cheeses Bayaslag and aaruul. Both are rock hard, but use acid to coagulate the proteins instead of rennet. They are often consumed after soaking in tea, or are sucked on, not chewed. Their shelf life is apparently over years long.

Just found that earlier today after doing some research inspired by this thread.