Can I still cook on my propane grill with rust?
Rust, or iron oxide, is not poisonous, unless consumed in large amounts. Thus it is relatively safe to grill on your barbeque.

What about the people who get cut by rusty nails and get lockjaw? That's not due to the rust, but rather, due to the bacteria on the rust, which is called, Clostridium tetani, which is found in the soil, and presumably, the nails have had come in contact with the soil, and so actually contains some of these deadly bacteria, and so, when a wound is made by the sharp object, the sharp object(nail) will also infect the wound causing tetanus, or lockjaw.

Which is totally irrelevant to your grill, as I assume, it hasn't actually come in contact with the soil has it? 

So, it's safe, relatively