The mordant is the whole difference between a dye and a stain
What a mordant does
Binds the dye to the fibre. Alum is the usual choice, is not hazardous, and works on wool and silk straightforwardly.
Cellulose is harder
Cotton and linen need a tannin step before the alum. Skipping it is why beginners get pale results on cotton and strong ones on wool.
Testing
Dye a small sample and wash it three times before committing a whole garment. An hour of testing saves a great deal of disappointment.
