The article suggests glass shampoo bottles? No thanks. Plastic is a great material, it is just abused.
Getting a bulk supply that doesn't use plastic (or send you to some funny store that you have to drive further to and that costs more) is presumably the hard part...
Natural soap does work well on hair.
Soap occurs in nature?
Regardless, I think his point is that shampoo as we know it today is very much a product of the modern marketing/industrial complex.
Plastic avoidance should first target plastics that can't be recycled.