I've encountered a -lot- of people who comment on the funny hats in religion.
Y'know the weird thing? Nobody comments on the fact that hats play a role in -every- religion. They also play huge roles in official government positions.
"Well, yeah," you might say, "they're part of the costume, part of the uniform; it helps define people's expectations of who you are and what you represent."
That's true, of course; that is part of the role of a hat. But see, you're underestimating the cleverness of some people who lived a very long time ago.
Why, pray tell, are non-clergy men traditionally forbidden from wearing hats in religious gatherings - and why are women frequently permitted them? Why are hats traditionally forbidden in schools, government buildings, and the home? Why do clergical hats typically lack a brim?
Do you think your personality is different on a sunny versus a cloudy day? Outdoors, versus indoors?
Hats - brimmed hats in particular - have a -huge- impact on your mood and personality. I don't say this because I've read a study - I don't have to. A hat doesn't just darken your face - it darkens your mood. It makes you less empathetic, less vulnerable, more insular. You know the person who refuses to ever take off their hat? It's because removing it leaves them exposed and vulnerable; it's probably the only thing that lets them comfortably interact in public.
A brimmed hat can easily turn 10-20% of your field of vision into utter darkness. What do you think that does to a police officer wearing a hat?
What do you think it's done to our society that hats have vanished from common dress over the past sixty years?
And trust me, this isn't a unique insight. Social engineering can be as simple as popular figures no longer wearing a hat, setting fashion, and thus social, trends for decades to come.