How do you keep whites white without bleach?

Add a cup of white vinegar to a full load.

Add salt to your laundry water. Premix the salt in a large container using hot water to melt the salt. Make sure the salt is completely mixed so you don't get residue on your clothes and in your washing machine. Salt not only makes your water softer, it also removes many stains. If you need more information about salt water...go to a place that sells water softeners for home use or go to a place that sells salt water for swimming pools for more input. Rinse your laundry tub when finished with clean hot water.

Biz it’s the best

I use a cup of white vinegar.

Borax is a really good detergent to use

Oxyclean or hydrogen peroxide. (Something basic!)

https://www.thespruce.com/how-to-keep-white-clothes-white-2146392