If I am logged in, I can see that on the user's profile page, the hat is visible. But if I open the profile URL of the same user after logging out, there is no hat on the gravatar. Shouldn’t it still be visible?
This is the case on those sites were you only get hats when you opt in, either by clicking "I love hats", or by simply wearing a hat. These sites are:
For Stack Overflow, the reason is mainly performance; for the others it's because the sites didn't opt in to showing hats by default. Math Overflow is completely hatless.