I use a mix of things. Liquid soap flakes with a teaspoon of dr bronners salsuds (found salsuds on its own made washing a bit hard but liquid soap flakes on own does not get everything clean. (Salsuds is fab by the way for loads of household cleaning inc carpets!).
I also use hydrogen peroxide mixed with bicarbonate in the pre wash cycle or as a soak for whites and stains.
Plus because I am very sweaty I use a spray bottle with 1 part washing up liquid (I use bio-d which is fantastic - I also use this as a hand wash in the kitchen and to wash my hair as it's the only thing I've tried that doesn't set off my seborrhiec eczema), and 2 parts hydrogen peroxide as a pre wash stain remover spray and on all arm pits. . If I use this I also add a half scoop of Dri-pak laundry boost to the wash to create the oxygenation. Am going to try bicarbonate soon instead to see if this is as good as it will be cheaper.
I use vinegar as a fabric softener but it isn't perfect so have recently started using Attitude fabric softener as it is rated A by the EWG even though it does have some ingredients that are less than completely non toxic. Am fed up with crispy or bobbly clothes though so have chosen to make that compromise. It hasn't flared up either of mine if my husband's skin condition.
I've done a lot of testing and trialling of different products and the above is working well for me at present.
Be aware that eco friendly is NOT the same as non toxic. A number of Ecover products contain things like phthalates which you don't want anywhere near your skin for example! I believe Ecover zero products are pretty good toxicity wise but don't have good reviews in terms of effectiveness.
If you are concerned about toxicity and/or skin safety check out the EWG health cleaning database. Even if the product is not included, you can search on individual ingredients. A full ingredient list must be provided under EU law (for now anyway!!!!). so ask the manufacturer if it's not on the packet.