As others have pointed out, the basic chemistry for B&W is pretty safe when common sense is used. But some photographers eventually begin to delve into the "dark arts" of mixing their own chemistry which involves working with raw compounds that can cause problems if not treated with respect. if one reads the MSDS for catechol ( you might just run, not walk away even though it is a compound in one of the best film developers you can make from scratch or from a kit.

As you move into the various realms of alternative processes, you begin to work with various carcinogenic compounds and heavy metals. Wet plate collodion uses a bunch of potentially harmful chemicals from cadmium, to silver nitrate to KCN yet it is one of the most rewarding of all photographic processes. The key is to treat all chemistry with respect and research any new process thoroughly with regards to the handling of chemicals.