Absolutely! The dishwashing liquid is super strong, great for emulsifying oils and crap, not great for hair!
I use that c68 or whatever it is, then the fairy liquid, then shampoo and conditioner, blow dry- lick of alcohol- dry-tape-whack it on
I do a complete re & re once per month, but redo the hairline myself weekly. I usually shampoo the hair and condition just once per week as you don't want to dry out the hair prematurely. I shampoo before I re-do the line so that I have clean hair for at least 24hours while the bond cures.
I definitely would not use the liquid soap, its too harsh and you want something formulated for coloured hair.
After I re-do the hairline I spray some leave in conditioner to combat any alcohol used in the process.