"Bright light can never hurt your eyes" seems false to me… enough energy focused on the retina will cause damage, regardless of the wavelength. Otherwise you would not need to wear laser goggles…
That aside, materials typically have certain ranges where they absorb light more strongly than others. There is no hard and fast rule for this, but if you google "absorption spectrum glass" you will hit tons of pictures, including the following one for borosilicate glass:

this shows a nice flat transmission "window" from about 300 nm to about 2200 nm, covering the near UV to the infrared. This means you would see the glass as colorless, but that doesn't mean all wavelengths get through - just the ones you can see.
As for gamma rays - their energy is SO much greater, and their wavelength SO much shorter, that the mechanisms for absorption are quite different. Typically, they no longer interact with the electrons in molecular bonds (which are responsible for most of the behavior of material in the visible spectrum); they are not even interacting with the bound electrons of an atom (or rather, the binding energy becomes unimportant when the gamma ray energy is on the order of MeV); instead, they act like particles that may bounce off other particles (mostly electrons) like billiard balls - they scatter, and impart some energy to the electrons. This causes ionization, which is why this is called "ionizing radiation".
The retina will be damaged by too high an intensity of visible light: the energy will cook the proteins, and they will not recover. Recall that retinal detachment is corrected surgically by laser - "spot welding" the retina to the back of the eyeball with a bit of cooked tissue. That bit of the retina will be blind, but if it stops the rest of the retina from flapping around it's a small price to pay. This is done with an argon laser which is in the visible part of the spectrum.
The cornea will be damaged by UV. Have you ever heard of snow blindness? The intensity of sunlight in the presence of snow (lots of reflected light) can lead to "sunburn" of the eyes. That's what Feynman protected himself against, presumably (see the above plot - glass typically absorbs in the UV).
There's much more to say about this topic - but for now I have to leave it here.