What is the hash rate of the Bitcoin network that causes maximum difficulty?

The hardest possible goal is all 0 plus 1 (0000000...1). If such a block were ever mined (which is highly unlikely – on average it takes 2^255 hashes per 10 minutes, or 9.6e73 hashes per second), the network would definitely crash. This means that only one block can be mined at that difficulty level.

Of course, if the target is 0, you won’t be able to mine any blocks at all.