I had my hair trimmed today. My hairdresser and two other ladies in there all use a homemade laundry detergent. One offered to bring me some and said it doesn't irritate her daughter's skin (my skin is also sensitive). I told her I was going to try it and wrote down the recipe.
When I got home, I looked it up to see what else was out there.
One site gave a breakdown on how economical it is. One said how to turn baking soda into washing soda if the baking soda isn't readily available.
The most challenging part for me seems to be that it makes a lot and would require storage containers.