This is a popular subject in salon talk. What is the difference between hard water and soft water anyway? The hardness of water determines whether water is hard or soft. The hardness of water depends on the level of calcium and magnesium content. The higher the concentrations of minerals, the harder it will be.

Most regions of Japan supply soft water. On the other hand, I think most of the water supply in the US is hard water, at least in California.

What the hard water and soft water do to your skin and hair?
Soft water leaves skin and hair soft and moist. However, hard water makes hair feel rough and leaves the scalp oily.
The reason why hard water has such an impact on hair is the mineral content in water. Mineral contents make shampoo lather not so well and leave soap scum as the result of combining with surfactants.

There are some solutions to protect you from it.
Installing the water softener and the shower head are good ideas, but I have a better idea!
Use shampoo that is good with hard water. Nonionic shampoo will be your savior! Nonionic surfactants don’t combine with minerals and affect hair and skin protein. It helps to leave them soft and smooth.
Those are the nonionic surfactants.

Decyl Glucoside
Lauramide DEA
COCAMIDE METHYL MEA

CRES Gemme, Lishe, Ricca shampoos contain those ingredients. If you have trouble with hard water, try those shampoos!