Are the precautions gods take to ensure their priests don't infect heathens with lethal diseases adequate?

Apparently not in this case, or any other. The Europeans didn't know it at the time,but just the initial contact would have decimated the whole Western hemisphere. Just wait 5-10 years and move in. They could have avoided all the wars. It's safe to assume the missionary knew he was carrying sickness and death in his pockets.