[AlexandrB]

I thought water softners typically used an "ion exchange resin"[1] where the hard water (magnesium, calcium) ions are swapped for sodium ions[2]. So you should be able to taste some sodium.

[1] https://en.wikipedia.org/wiki/Ion-exchange_resin

[2] https://en.wikipedia.org/wiki/Water_softening#Ion-exchange_r...