Women are not bound by the same hat etiquette as men. Men are expected to remove their hats in most situations where it's perfectly acceptable for a woman to wear a hat. Manners and custom have loosened over the years, and for women, almost anything goes. Women's hats are seen as fashion accessories, part of their outfits in many cases. According to The Red Hat Society, "women are generally exempt from removing their hat, particularly if their hat is fastened to their hair and difficult to remove easily."
Men should always remove their hats during the National Anthem, but women follow different rules. If a woman is wearing a very formal or fashionable hat, she is not required to remove it, explains Hats in the Belfry.com. If a woman is wearing a baseball cap or a very casual hat during the National Anthem, she should remove her hat.
When a woman wears a hat inside a church, it demonstrates respect and fashion sense. The opposite is true for a man. Women are not required to remove large hats in churches, but should be considerate of people sitting nearby. Even though it's perfectly acceptable for women to wear a hat to church or a funeral, if a woman is dressed in very casual clothing like jeans and wearing a baseball or men's style hat, it's considered polite for her to remove her hat.
Women are encouraged to wear hats at formal teas, luncheons and weddings. As a rule of thumb, the earlier in the day, the wider the hat brim. It's considered proper to wear a wide-brimmed hat only in the day while the sun still shines. A large-brimmed hat, such as a sun hat or a floppy straw hat is inappropriate for a restaurant at night because there is no sun. Smaller hats like berets, fedoras and newsboy caps are considered appropriate evening wear when dining out.
A woman may wear fashionable hats into a theatre (movie theatres included) if the people behind her don't have to struggle in order to see around the hat. It is common courtesy to remove hats when they might block someone's view of a stage or screen. If there's nobody behind you in a theatre, keep the hat on.
How to Remove Your Hat
Advanced Etiquette.com says the correct way to remove your hat is to hold it so only the outside of the hat shows, not the inside and lining. If you're taking a hat off for only a few moments, hold it in your right hand across your chest and heart. For longer periods, place the hat on a surface, with only the top and outside of the hat showing. It's considered impolite to reveal the inside lining of your hat.