So, I'm going to guess you are in the "purple" area and get your water from groundwater. It averages 21 grains per gallon and goes as high as 30.5. Tell me if I'm wrong.
Just so you know, 25 grains per gallon is considered "very hard" by the USGS. Other sources say 15+ gpg is extremely hard. My water was crazy hard at 23 gpg. By any measure your water is exceptionally hard.
Re: Chemicals:
It's all chemicals. All of it. Every bit of food, every breath, every beverage you drink. You are made of a bunch of chemicals.
Water softeners exchange hardness ions (calcium and magnesium) for sodium ions. Sodium is in most of the food and beverages you consume. Soft water has less sodium than bread, milk, etc. and certainly less than fries from the drive through.
How skin feels after a shower with soft water is how it's supposed to feel. That's what it really feels like. You are used to soap scum on your skin. Soap scum is soap, combined with hardness in the water (calcium and magnesium) that forms a really nasty layer of crap on your skin... and everything else, such as your hair, shower, tub, toilet, dishes and clothes.
Soap scum and hardness deposits in general make everything hold dirt. It creates a rough surface that everything sticks to, such as "skid marks" in your toilet. It makes your shower doors and tiles get nasty. It makes the insides of your dishwasher nasty. It makes stuff stick to your bathroom and kitchen sink.
I'm not world's best housekeeper, but my kitchen and bathroom stay so much cleaner since I got my water softener.
Q