>Shakespeare's entire vision of the world is intrinsically Christian.
This is just not true. I refer you to several sources if you really are interested in this topic:
Shakespeare: The Invention of the Human by Harold Bloom
Naming Thy name by Elaine Scarry
https://www.amazon.com/Naming-Thy-Name-Shakespeares-Sonnets/dp/0374279934
Shakespeare was nominally Christian or a cultural Christian as everyone was in Elizabethan England. However, there is scant evidence to suggest he was in anyway devout. He was certainly not pious--that's an obvious fact. He was openly antagonistic to many Protestant ideas. It was Protestants after all who protested the Globe theatre and the "ungodliness" of his plays.
>The common misconception is that these are made-up stories to explain the unexplained. In some respects we are a very blind culture that projects in blindness onto other peoples.
Non of these Gods are real. They arose from human culture as a way to explain natural phenomenon like the sun and moon, thunder and lightening. Gods were the inventions of humans.