I have a water softener. That's what my cats drink (it's what we drink).
There has never been issues, my house is 27 yrs old and the cats who have always lived there since my youth (I bought my parents house so basically I've had the house for 27 yrs... in a way) have never had health problems.
The only thing I've noticed is, 4 of my 6 cats are kinda fat. My mom's cats also were fat. Mom however does not have a water softener at her new condo; she's been there for 1.5 yrs, and well, her cats are still fatter than ever (and her doggie is also plump!) so I don't think the water affects them.