Agreed that hats should not be worn indoors.
If the pic is where I think it is (Buttermilk Channel), it's a pretty casual restaurant. I still think people shouldn't wear their hats indoors, but it's hardly a coat and tie kinda place. It's also in brownstone Brooklyn, land of the Man-Boys (and I say this as someone who lives in brownstone Brooklyn... It's very unfortunate to see a 40 year old man dressed like a child, but that's the de facto uniform here).
I will lament the decline of places requiring a coat and tie though. There are very few of them left, but I do appreciate them even more for it.