It's that just a dad thing in general though? Dads tend to hate everyone that their daughters are seeing, dating, sleeping with.
I also think there is an unwritten rule where Dads pretend they don't kow what their daughters are up to and daughters pretend to be daddy's little girl forever.
Anyways, Futaba isn't his real daughter, and he only takes care of her out of guilt ( i didn't complete his social link so not sure if anything is developed on that front, i was too busy boiking all the womens, living out my fantasy amirite). I'm pretty sure he hasn't seen that much of her since she's been living with him. Sojiro owes the protagonist much more since he got Futaba to actually go outside. So I'd think Sojiro would let it slide ( no pun intended).
Yes i know, I'm a horrible person.