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?
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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.