I'll just add my personal/professional perspective. I have worked and taught for many years in biochemistry labs, where the range of chemical hazards is on roughly the same scale as in a darkroom. (Some things we use are more hazardous, like concentrated acids and bases and some more specialized reagents.)
In the lab, I always wear safety glasses and insist that students do so. But, my definition of adequate safety glasses, in this context, includes the prescription glasses that I wear every waking hour. If you don't wear prescription glasses, there are inexpensive safety glasses available at home improvement stores, for instance, that should be fine. If, in spite of safety glasses, you manage to get some Rodinal in an eye, flush it well and get medical attention, as advised by others.
Until I started using Pyrocat developer, I never wore gloves for developing film or prints. After investigating the potential dangers of Pyrocat, however, I decided that nitrile gloves would be an appropriate precaution. I would probably use them now for other developers as well.
Just to lighten the tone of the discussion, here;s a story that I heard over 40 years ago at a workshop sponsored by E. Leitz (long enough ago that E. Leitz was the company that made Leicas!). The instructor demonstrated developing negatives with Rodinal and used a syringe and needle to remove the concentrate from a rubber-stoppered bottle (another sign of how long ago this was). In the patter that went along with the demonstration he said that a co-worker once accidentally injected himself with a few mL of Rodinal and started turning dark. But, once someone injected him with fixer, he cleared right up and was fine. Another reason to always use fresh fixer.
David