My thoughts are: Stop bothering to rehydrate. The small amount of softened water won't hurt anything if you do. If you are still concerned buy a gallon of spring water at the store.
One home we owned had well water with a lot of iron in it. Didn't taste good and left rust stains on the fixtures so I installed a softener. I usually bypassed the softener for brewing but depending on the style sometimes mixed it 50/50. Back then I was kind of winging it on water but the beer turned out fine.