Sodium chloride is pretty much table salt as you know and love it. It shows up in a lot of personal care products and is useful as an astringent and antiseptic ingredient.
However in shampoo its main job is to work as a thickener and to help keep all the ingredients nicely mixed together (or emulsified).
A lot of shampoo ingredients are very fluid, which means judging the right amount to pour out of the bottle can be tricky if it just runs out and off your hands.
Thickening the consistency of shampoo (and other detergents you might use such as liquid laundry soap or dish soap) makes it easier for the average person to control to get the right "dose" every time.
There are articles on the internet promoting the idea that if you add salt to your conditioner your hair benefits. All it does is make your conditioner a bit thicker in consistency. It does not actually do anything good for your hair. And, because salt is more soluble the warmer the water, it is probably rinsing straight out of your hair again, so basically not doing anything at all.
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