Patch fiber is usually using Class 1 or Class 1M lasers which are entirely safe to look at. Also the light spreads out very rapidly at the end of an unterminated fiber because there's no lens to focus it. So don't hold it directly up against your eye but like a foot away is fine. The lasers are less focused (i.e. cheaper) and the multi-mode fiber is wide so it spreads out very quickly. You can't actually see the IR light, the red light you see is just sidebands of the signal.

Fiber used for long hauls is much more powerful but uses a wavelength that the human eye is very good at blocking (so your eye dissipates more of the energy but what does get through could damage your retina). There are systems that will decrease the power if the link is lost (cut or unplugged) to protect eyes. The light will still dissipate in free space (because there's no lens) so you should be safe from a distance. Single-mode fiber uses a more focused laser and more narrow fiber so it will spread less over a free space distance so don't get too close.

Always better to just use a light meter (or a phone camera) if you're unsure but also just holding the end of the fiber against some paper or your palm may reflect enough of the visible light to let you know the fiber is live.