Only happens when logged out:
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Good catch 
Probably easy to fix. It’s because of this rule. If we remove it, the issue disappears:
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Additional info: while the input doesn’t shift when hovering the button when logged in, there’s a pixel-sized white flash in the button’s bottom corners:
I think it’s linked to the same issue, and we see the behavior better if we increase the transition duration here:
Another fix could be just dropping all of the changing border and padding declarations that happen on header icons on hover and selected states… 
It looks clean by default, but once you change a size or icon it pretty much falls apart.
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