I think each situation is individual and needs to be treated as such.
When I had my DDs, my mother was there with both births - and she helped me through them both.
With DD1, MIL came to visit baby at the hospital, FIL chose not to.
With DD2, I had no visitors at the hospital, but that was due to a 3rd degree tear, physiotherapy, catheter and me basically being a mess. I wasn't up to having visitors, and so didn't have any after the birth. ILs included. It was bloody, it was messy, it was not a pretty sight. Eventually, when I did sign myself out of hospital (against consultant's advice, but I couldn't cope there anymore), I invited ILs over as soon as I got home. FIL didn't come as he went to gardening club, but MIL came and had me making her a cup of tea, literally hours after I came off the morphine. (Whilst I was struggling making her tea, she was cooing over the baby!).
In my situation, my mother was there for me, my MIL was there for the baby. If they act differently, they get treated accordingly. End of.
So no, I agree, no right.