I have moderately hard but very high iron water straight from the well (its orange). I'm on acreage on the high side of a swamp/wetlands with a small lake/large pond about a half mile down the road and uphill. No issues with water availability but the mineral content is quite rich. I haven't had a full water report done, only a free test done by the supply house I bought my filters and softener from. I ran further tests using water test kits I had left over from when I kept a saltwater reef aquarium and basically maxed out the test readings on everything.
Long story short, I've done some experimentation with water. I carted 10g city water from a friend's house, used 10g unsoftened but filtered water from the well and 10g softened filtered well water. Three batches, same recipe. Favorite was the unsoftened filtered, followed by city water followed by softened/filtered well water. No major differences in flavor profile but noticed a different mouthfeel and some slight flavor differences. The softened water had a flavor that plagued my first several batches before the experiment. Can't describe it, it's not unpleasant but it is unwelcome.
I haven't done many all grain batches, not willing to make the time commitment so I do 75% of my beers with extract. But I did stop using softened water for all of them. Made a noticeable difference in flavor and mouthfeel. I did make one stout with water straight from the well. It was interesting, definitely could taste the "raw" water but it wasn't bad. A lot of people loved it and ask for it again, I think I was just looking for the flavor changes.