There are dedicated shampoo bars which are sulphate free and CG friendly. You can use any cold processed soap though from what I can make out, as the cold processed soaps are high in lovely moisturising oils. There are heaps of threads on here about them, if you do a search for "soap bars". They are all quite alkaline so most people do an acv rinse afterwards to seal the hair shaft back up. HTH.

3a, low porosity, protein sensitive, medium texture (with random coarse strands), growing out a pixie cut

Located in Tasmania, Australia