Making cheese without rennet
You cannot make mozzarella without some form of rennet.  It can be natural rennet, synthetic, or vegetable-based rennet, but you need it to get the correct cheese texture.
This goes for the vast majority of cheeses.  The only ones you can make without any type of rennet are the soft, heat-and-acid-set cheeses such as ricotta, farmer cheese, chevre, and paneer.