Behold the Brain Coat, which is not a tinfoil hat but rather a silver-coated nylon skull cap with ear flaps. It's lightweight, breathable, and claims to be effective at shielding the brain from radio waves while remaining comfortable even if worn with other headgear.
Microwave Shielding Effect: >35 dB at 1-10 GHz
Surface resistivity: <0.5 Ohm/sq
I put mine on whenever I go on Twitter and it works perfectly.
Brain Coat | RF Shielding for your Mind [Amazon link]