it contains a tiny amount of bicarbonate of soda (as used in baking powder and indigestion remedies), not salt.
The sodium count is lower than coke.
I don't know why people claim that the sodium level is above safe limits, but it isn't true.
If you are on a low-sodium diet, so you don't eat, for example, bread, cornflakes, cake or soluble paracetamol, then by all means drink hard water. Not bottled water, though, some of which contains more sodium than water from a softener. And if you have an FF baby who never touches marmite, hard water is probably better.
It is thought that hard water is better for the heart, so by all means drink hard water if you want to.
I did have a link showing the sodium content in a gallon of softened water, which is much less than in, say, a slice of bread, but I can't find it.