I would challenge your assertion that there are "a lot of non-physical realities in a purely physical world". What realities are these? Give concrete examples, don't just throw out the assertion.

For example, you could say, "I believe the mind is an example of a non-physical reality." I would disagree, but then we could argue about it.

In order to be intellectually honest, and atheist must also be an agnostic. It is impossible to PROVE a negative in any system of logic. However, it is possible to evaluate the evidence for and against a proposition, and come to a reasoned conclusion about the probability of that proposition.

Agnosticism is a statement about knowledge: I know there is/is not a god (gnosticism), or I do not know if there is or is not a god (agnosticism).

Atheism is a statement of belief: I believe there is a god (theism) or I do not believe there is a god (atheism).

I would argue whether one is a theist or atheist, one MUST be an agnostic if you are working by logic. If there is a god that exists and is omnipotent, he can make you believe anything, so we cannot trust any of our senses or any evidence. If you do not believe a god exists, it is impossible to probe a negative and you must admit this to be intellectually honest.