Update: Unfortunately, after a couple of weeks of using the soap nuts, I found water backing up in the washer. We suspect that the soap bubbles were causing a drainage block. Interestingly, the washer would be dry when we emptied the clothes out of the washer, and then water would gradually back up over the next few days. I'm still using soap nuts for handwashing and other uses. One idea would be to further dilute the mixture and see if that would mitigate the problem. Hopefully you won't have this experience!
One of the reasons I like to make my own food is because I like to know what I'm eating. I'd also like to know what chemicals I'm being exposed to - like in the laundry. I've long used powders, but while they do something to reduce waste and plastic, most still come in a plastic bag with a plastic scoop and lots of chemicals.
I've started using soap nuts. They're natural and organic. They do have a high carbon footprint as they come from Nepal, but this brand uses their funds to help women in that country. Beth Terry of My Plastic Free Life took soap nuts a bit further and passed along this liquid recipe. It's easier than pie, but you do need to keep it refrigerated...and labeled so someone doesn't mistake it for ice tea! I'm using this in my HE washer and my clothes come out clean and industrial chemical free.
And, while I use a clothes line, my boyfriend likes a dryer...and dryer sheets. He agreed to try a homemade and less toxic version. I cut up some used but clean fabric into 8"x*inch squares and keep them soaking in a large plastic used yogurt container with a mix of white vinegar and water. I've added a bit of lavender to give it a nice smell - and voila, a natural dryer sheet. You can reuse them indefinitely. Give it a whirl.