The standard explanation for how Faraday cages work is that the metal mesh from which it is constructed will let through only those photons with sufficiently small wavelengths to fit through the openings.
If a photon has a very long wavelength, it will not fit through the holes in the metal mesh. Instead, it is reflected or absorbed. Low energy photons, which are associated with long wavelengths, are thereby prevented from entering the cage.
This sounds reasonable at first reading. However, it makes little sense on closer inspection. Why should the fact that a tiny particle is oscillating at a low frequency have anything to do with its ability to penetrate a metal mesh with holes vastly larger than itself?
The alternative explanation is that the penetration of photons through the metal mesh of a Faraday cage has nothing to do with wavelengths. It is rather a function of momentum.
All detectable photons have a pilot wave associated with them. This wave extends out far beyond each photon, and it is this pilot wave that prevents low energy photons from getting through the mesh of a Faraday cage.
Low energy photons have insufficient momentum to push themselves and their associated pilot wave through the mesh. These are either absorbed or reflected by the mesh.
Low energy photon about to be reflected by a mesh
Higher energy photons have little problem pushing their pilot waves through the mesh. To prevent these, the opening in the mesh have to be smaller. For visible light, the mesh has to be as fine as the lattice of atoms in order to prevent penetration.
High energy photon pushing itself and associated pilot wave through a mesh
The mechanisms behind reflection and refraction of visible light is the exact same as the mechanisms behind the Faraday cage. Visible light gets reflected, absorbed or refracted by the atomic lattice of glass depending on their momentum.
For radio waves, the mesh of the Faraday cage acts like the lattice of glass, letting high energy radio waves through, while absorbing or reflecting the lower energy ones.
In the case of barriers made out of bricks and mortar, we get the situation where visible light is incapable of penetration, while radio waves go through. The lattice of the atoms in these materials are ordered in such a way that they obscure the relatively straight path of visible light while allowing the much more meandering radio wave photons to find ways to penetrate.
Low energy radio wave bouncing its way through bricks and mortar
This reverses the situation described for the Faraday cage and glass. The low energy radio waves bounce their way through the atomic lattice while visible light gets absorbed or reflected.
For a good introduction to pilot wave theory, watch this video.