Methodological Naturalism

How can we justify methodological naturalism. If gods are acting in the world, a methodological naturalistic bias would lead us to reject gods, demons, angels and other supernatural entities as explanations.

But how do we do science without assuming there is a natural order? How can we tell if something has a natural explanation or is of divine origin?
If miracles or other supernatural activity is allowed, the universe is no longer guided by predictable rules. If we conduct an experiment, we can never know if the results follow from the nature or caused by some supernatural being.
To allow for anything supernatural, we must reject science. We cannot have a world were the supernatural can act and where we can make accurate measurements and predictions about the natural since we are unable to rule out supernatural influence.
We can, however, assume that there is no supernatural influence. As long as our predictions and measurements are consistent, there is no reason to assume the supernatural in.
What about the soul? Don't humans and other intelligent creatures have a special aspect within, that is generally referred to as the soul? If such a thing exists, why would we assume that it is anything other then natural. If it is a part of us, then it is natural.