This doesn't align with my own experiences with hard and soft water. The water where I currently live is what I'd consider medium-hard. No significant problems with lime or other mineral build-up on faucets, showerheads, kettles, etc. but there is some build-up over time... enough so that I have to use distilled water in my espresso machine. And soap rinses off skin very easily.
When I visit places with soft water, I have difficulties rinsing soap off my skin. The water almost feels 'slippery' to me, as I'm accustomed to the microscopic mineral particulate in my usual hard water providing it with, while certainly not a 'gritty' feel, but with more 'resistance' that feels 'cleaner', if that makes any sense. I'm having difficulties explaining it.
Anyway, this relates to the brush and soap build-up in that I don't understand how you get soap residue in the brush with hard water (which, in my experience, should easily rinse out clean due to the 'abrasive' quality the mineral content provides), and how you get no build-up with soft water (which should not rinse out clean due to the lack of 'abrasive' action of water with less mineral content).
Or do I just have this all backwards?