Hello, 2wheeling: How are your roses by now? My guess is that your straight tap (unsoftened) water isn't as toxic for them, but the desert heat and dryness will eventually concentrate the mineral buildup around your plants to an intolerable level.
I'm surprised that your entire system is softened , since the process merely adds salt to your water in order to enable soap to lather for bathing and laundry; usually, only the hot water is softened.
Happy Gardening and Good Luck !