no problem with "gray water" at all
Indeed, I even re-use bathwater.
You all probably know that soothing feeling of a very hot bath that almost gets you this "sauna feeling" of being totally cleansed and soft as a marshmellow (the one that makes you want to go to bed right on).
Well, before the temperature drops too low I use a PE tank of 30 litres to carry it down to my washer and I will run a load or two in the prewash cycle. Shampoo and shower gel have a substantial capability of getting rid of superficial dust and dirt and they have a first run on oily substances. Great for heavily soiled items or workshop clothes, garden clothes and similar. If it was my own house I would have installed a gravity drain pipe to go down to the basement, into some tank for this.
Secondly, I run the hot wash in frontloader one, pumping it up and out to frontloader 2.
Stop on machine 1, waiting for machine 2 to get done (reheating it up again just a tiny bit)
Repeating the same with all rinse cycles and their respective intermediate spins, apart for the last rinse.
This is done with fresh water always (and some softener or laundry scent, just as needed).
Result: Utility back payment of almost 500,- Euros for last year. 486,- that is.
Of course: This will work only for similarily lightly soiled loads of if you just want to do a quick "freshen up" cycle. You get 2x full prewash, hot wash, 4x rinse and spin for the cost of one.
I admit: On heavily soiled items, it won't work: The first wash water is dark gray and smelly (and I want to get rid of it). Same thing with infected clothes (my brother was in the clinic for some severe surgery, all his wash got a new and fresh fill of water for each single load.) Imagine the blood and what have you.
Yet, for regular stuff, re-using is a standard here. (You won't believe our utility bill rates).