As it's dangerous to accidentally look in a fiber optics, what does one normally use as a protection to this while working with fiber optics? Are there safety glasses for such things? How is that problem handled in practice?
Disclaimer: I'm not a safety inspector, but I have been handling fiber-optics almost daily, without mishap, for nearly 20 years.
The danger is there, but shouldn't be over-hyped.
A laser-pointer is much more dangerous.
In my opinion: All the warnings in the manuals and on the packaging are more intended to make sure the manufacturer can't be sued into oblivion by some lawyer in litigation-happy USA.
As for safety glasses. I have never heard of them. I don't think they would work either. You would need something equivalent to a welders-mask, meaning you can't see anything at all when wearing such glasses.
Also worth noting - the labeled hazard is generally for optics actually using lasers. This is, in most cases, for single mode - which, in addition to being quite a bit more powerful, also is at a wavelength not visible to the human eye. The problem here is, in part, that there isn't really even an immediate pain impulse to tell you there's a problem. Multimode, in contrast, is much lower power and is transmitted via an LED on a wavelength visible to the eye. It's still not a great idea to look into such an optic, of course, but it's not dangerous enough to warrant the warnings of various SM-based media.