Great article, I enjoyed the perspective of looking at the chemistry!
One of my favorite substances to use is the old timer's cleaning agent: Borax.
A 2001 study found that an estimated 10% of the population has their health adversely affected by liquid laundry detergents, especially as the volatile gasses out-gas in heated driers ( https://www.sciencedaily.com/releases/2011/08/110824091537.htm ).
To make maters worse, as far as I know, there is no regulation that states that these companies have to list everything that they use on the label. Therefore, one really has no way of knowing exactly what is in these chemical detergents.
I just recently switched to natural deodorant, and we've used natural detergents for quite some time.
Super comment @jzen, thank you.
Well, be careful though. It is not because a product is 'natural' that it is not toxic or eco-toxic. For example, I use Alun stones as deodorant under arm pits. But I do it very seldomly (a couple of times a month). Although it is natural, it contains al3+ salts which are carcinogenic!
I also notice that since I stopped using deodorant, I do not need it, and I don't stink!
For all alternatives you wish to use (like borate), Look for and Check the MSDS (material Safety Data Sheet).
For example Borate tetrahydrate (Borax) appears OK, but its acid version is pretty crap... So be careful.
Borate: http://www.sciencelab.com/msds.php?msdsId=9924967
Boric Acid: http://www.sciencelab.com/msds.php?msdsId=9927105
Check sections 11 and 12 for more detailed toxicological info.