Softened water is safe to drink for most adults. The sodium level added by domestic softening is low, well within WHO guidelines, and negligible in the context of a normal diet. The practical standard for UK households is to leave one kitchen cold tap unsoftened — preserving access to hard water for drinking and infant use, while the rest of the house benefits from soft water.
If you are in a specific at-risk group — medically supervised low-sodium diet, or making up infant formula — use the unsoftened tap for those purposes and you have nothing to worry about.