Seems to me in the US these days in some churches you're more likely to spot a Hooter's t-shirt than a hat.
My maternal grandparents were milliners in the first half of the 20th century, starting in an era when no self-respecting person of any age would go outdoors bare-headed. When I was growing up in Kansas women and girls still generally wore hats and gloves to church and some wore them for shopping, in restaurants and to club meetings and such - any time the other ladies might see you and think less of you if you didn't try to look prim and stylish. It was understood that as an expression of individuality a well chosen hat is hard to beat.
Is this just me? When I watch old movies I have the impression that hats on both men and women made them look older than they were.