I didn't read it all, but most of those animals listed are already restricted in the State of Calif. And it is already illegal to have a desert tortoise unless you register it. I didn't read through to the end to see if you could get a permit in Arizona.
I don't know the regulations for keeping desert tortoises in Arizona, where you live, but I'm sure that if this law passes, you will be able to keep your tortoises under the "grandfather" clause. That's what happened here in California when our law passed saying it is illegal to take tortoises from the desert. We were able to keep our tortoises, and we had to apply for a permit from the state department of fish and game.
If I am reading this correctly the possession of cattle, sheep, and goats is illegal as well as dogs, cats, and even chickens. Oddly enough you can possess a rhinocerus or tapir and any of the cameloid group. This looks like many of the laws drafted by ignorant (of animallife) lawmakers.
Everone should go and get a Rhino, maybe with everyone keeping Rhinoceri they would ease up a bit?! I do believe that the Malayan Tapir is supposed to be very friendly if it has been 'captive'