Most likely, the local water department has info on how to use gray water safely for plants. The info will include something about appropriate soaps also.

With "the official word" in hand, you may gain some headway against your parents' resistance.

Whatever you do, do NOT use the commercial or home-made ones with borax in them. The boron builds up quickly and is toxic to plants.

Use as little as possible.

Most detergents are OK to use, even the commercial ones. Look up California Grey Water and see what they say.

We have a bin to collect laundry water and a pump to get it to the garden. We don't use detergent, but laundry disks, which are more common in Europe, but available here. Regards, Peter.

I never tried that but I did use ecos brand. it cleaned well and had the best garden that year. I don't know about any regulations against graywater here but definitely would check into it first where you are.
kim

Years ago, my grandmother ran all her grey water into the garden so as not to overwhelm the septic system.

I am not sure what her detergent was but my mom used Ivory Snow back when it was soap....so I guess that is a good guess.

She always made a nice garden.

I can remember as a kid my Mother's cousin used a wringer washer and 2 rinse tubs. She drained all her wash and rinse water into her flowers. She had a lot of flower beds, all kinds and vegetable too but the vegetables were too far from the house to water plus way too many for the amount of water she used once a week to wash.

Her flowers were always so pretty and never any bug or disease problems. Not sure what detergent she used but suds or rinse water never hurt hers--in fact she said it helped them.

All of our house gray water, which is all drain water except the toilets and kitchen sink, goes into the yard. The system has done so since 1992. The only thing we do not use is pure borax laundry aids. We make no other efforts to limit what cleaning materials we use. The plants receiving this water do quite well; we've never seen any ill effects from any household water draining activity, including the use of a variety of detergents, drain cleaners, and soaps. This system significantly reduces the load on our septic system, as well as putting all this water to a better use. I highly recommend such a water diversion if your plumbing allows. Our gray water system was an integral part of the house construction: there are two drain systems in the house.
Renais

I wouldn't trust the local water department. It's all about what products you use, and most are out of the question. Good luck!

Here is a link that might be useful: Carrot a Day

It seems that the surfactants used in detergents would be the one beneficial element in the gray water.
I'm not aware of any toxins that would harm the soils, even in the modern detergents.

Are there chemicals in modern detergents we should be leery of?
I wouldn't want to be wearing those toxins on my clothing either.