How do you neutralize detergents from domestic grey water?

You get a water purifier or a softener. (A water softener wont "neutralize detergents from domestic grey water." Indeed, a softener will do the exact opposite since hard water neutralizes many types of detergents.)

Depends on what you mean by "neutralize". If you mean make the detergent no longer function as a detergent, then depending on the type of detergent there are a couple ways.

Most detergents are the conjugate base of an acid. Acidifying the solution neutralizes the base and generally significantly reduces the ability of the detergent to act as a detergent. So, simply adding acid will often "neutralize" detergents. Large amounts of vinegar, or much smaller amounts of a strong concentrated acid, can be used.

Another method of neutralizing detergents is by the addition of divalent cations such as calcium++ or magnesium++. Many detergents strongly bind to these salts and, like adding acid, the resulting compound no longer acts as an effective detergent. This is why most detergents work better in "soft" water than they do in "hard" water. Hard water contains enough divalent cations to tie up the detergents molecules making the detergent must less effective.