Of course it is okay for the father to stay home and be the primary caretaker. We did it for a little while when my oldest daughter was 18 months old. I was able to find a job and he wasn't. The two of them were fine and both had some wonderful adventures.
There is no reason that a woman has to be the one who stays home if it is more prudent financially for her to go to work.
My daughter works, and her husband is a cabinet maker and his shop is at home. He takes care of his children, feeding them, providing for their needs. And they have flourished under his kind and patient care.