Whatever reason the father had on his mind, that is not enough reason to reject the gift from his son, if the child has not given any of his family and relatives anything at all, they would have said he doesn't have the love for his family. Let's say Religion must have been the father's excuse in the first place, he should have accepted in public and explained to him in private the reason for his objection to the money, I don't see any reason the father should reject money at all.
What if there is a strong reason which is valid like their religion prohibits it? Even though if it's a gift that came from my son, I will also choose to reject it. I know it can hurt me and my son's feelings but as long as I explain it to him on why did i do it, I think he will just understand it. Religion must be the center of all.
We must respect it because if not, bad karma are going to hit us. It's not about the money. Even if we have loads of it but if a severe ill hit us due to our actions, our money can't do anything to cure it. If they don't have a money but as long as they are doing a good thing, a good karma will just occur on them, making them earn better in the future.