Shielding is something I can speak to.
In theory EM currents can only travel on the surface of a conductor, but it is not perfect.
For a given conductor there is skin depth. The depth EM radiation will penetrate into a conductor. It is frequency dependent.
A Faraday shield blocks alternating electromagnetic fields because the skin effect confines induced electrical currents to the outer surface of the conductor, preventing them from reaching the interior.
Y8b can look up ski depth of aluminum and copper foil for cell phone frequencies.
en.wikipedia.org
Microwave ovens are in the range of 2Ghz. Microwaves. Some cell ophones are in micove renge.
Risk is disproportional to wavelength. Back in the 80s unshielded industrial plastic bag sealers using microwaves caused damage to eyes.i It can cook eye fluid and cause cataracts.
At high enough frequencies EMR can break bonds and disrupt cells.
Certain electromagnetic (EM) frequencies pose a risk to the eyes when intensity or exposure time is high, ranging from thermal heating via microwaves to photochemical damage from ultraviolet and high-energy visible light
Risk: High-power or close-proximity RF/microwave fields can cause dielectric heating. Because the eye has minimal blood flow to dissipate thermal accumulation, high-intensity exposure can lead to internal tissue stress and cataracts
And that leads to the debtes over studies and claims. JHvang word in RF and nicroves in re 80s I had te vew anjy chrnc radiation is to be avoided. Part of it came form a Russian study I read based on experiments dieone on 'prospers' as I recall.
I would not walk around with a cell phone next to my ear all the time. Radiation decrease by te inverse square law.
Testing a shelf hat would be straightforward. I'd have to look it up. You might be able to put a few layers of aluminum foil inside your hat ...
Easy to test. Turn on your phone and tape together a spherical shell of aluminum foil around it. Try and call the phone.
I used aluminum foil at times as a temporary shield fix for EMR problems.
he EMR standards I dealt with were ANSI and ISO standards.
Core International Guidelines
• ICNIRP Guidelines: The International Commission on Non-Ionizing Radiation Protection sets widely accepted scientific exposure limits for radiof requency and electromagnetic fields (covering 100 kHz to 300 GHz) to protect against thermal and electrical health effects
IEEE C95.1 Standard: Published by the IEEE Standards Association, the IEEE C95.1-2019 defines safety limits for human exposure to electric, magnetic, and electromagnetic fields from 0 Hz to 300 GHz
The standards are probably not free.
An IEEE summary
Section 4 exposure limits and table 1,2. V\m is volts/meter.
The IEEE is a major respected organization.
The shield hats are not pseudo science, they may reduce exposure. The are known radiation risks. The question is the cell phone risk.
Technically I take a Faraday shield to be a continuous closed surface. A beanie would not be a true Faraday shield.