So let me then say that atheism is a lack of religious belief, a lack of belief that there is any supernatural power in the universe. Whereas what the BSA requires as a condition of membership is that one does believe in a higher power, a supernatural power that is beyond the material plane. It need not be incarnate. This would be religious belief, or religious faith.
An atheist, believing that there is no God due to lack of evidence, has a belief, but he or she has no faith (being belief in the face of a lack of evidence).
But while the BSA requires a religious belief, it does not require a belief in any particular religious faith. Thus, it is within the letter and spirit of the First Amendment, which is meant to prevent the State from supporting any particular church or faith over any other, and preventing it from interfering from anyone's profession of any religion. The BSA does not do so, and there should thus be no impediment with it's doing business with the State.
I expect the BSA to appeal this decision. I certainly hope they do. And I'll bet that if they go all the way to the Supremes with it, they'll win.