https://www.researchgate.net/post/Cysteine_vs_Cysteine-HCl - this was discussed before. Its all about solubility. If you want to prepare a separate solution and add it after autoclaving, you will probably have problems dissolving it. I have added 0.5 g/L cysteine before sterilization and it worked fine for anaerobes like Clostridium.
Reducing Agent Solution: Composition per 110.0mL: L-Cysteine·HCl·H2O ..................................................................... 2.5g Na2S·9H2O.................................................................................... 2.5g Preparation of Reducing Agent Solution: Add 110.0mL of distilled/ deionized water to a 250.0mL flask. Boil under N2 gas for 1 min. Cool to room temperature. Add L-cysteine·HCl·H2O and dissolve. Adjust to pH 9 with 5N NaOH. Add washed Na2S·9H2O and dissolve. Distribute in 10.0mL volumes into tubes. Autoclave for 10 min at 15 psi pressure–121°C.