Personally my husband was an equal parent as far as I was concerned, right from day 1. If we want to talk about problem that start at birth, mothers excluding fathers from decisions from the off is another thing that can lead to problems in the future.
I am not projecting anything, thank you, but no, fathers are not equal from day 1.
It's biological, a father might be a bit tired but ready and happy to receive visitors, why wouldn't he. Meanwhile, the woman who has just gone through labour, given birth to a baby, with hormones all over the place, bleeding, and feeling exhausted and very vulnerable, some struggling to establish feeding, that woman might want a bit of privacy.
And you know what, she wins. Her needs and her wishes come first.
If her husband has major surgery one day, and asks for privacy, then in the same way, he gets to decide.
My point was that if things start badly from day one, they don't improve by the time the child is 4. If the MIL we read about on this forum were more respectful from birth, the relationships would not be so strained.
A mother WILL always pull the "I am in charge" card, because.. she is. The discussion was not with the father, who by that time is equal parent, but with a grand-parent who is most definitively not in charge of anything.