I noticed all my clothes staining so we installed a water softener, which has stopped the staining. Does the water softener take any of the manganese out of the water?

In general, water with high levels of the dissolved elements of calcium, magnesium, iron and manganese, referred to as hard water, are replaced with sodium ions in the softener unit, eliminating the hard water problem. Depending on your softener, when the zeolite (an ion exchanger) or a chemical matrix (a bed of plastic beads in the softener unit that removes the dissolved elements and replaces them with sodium) in the softener contains nothing but dissolved elements, it's time to regenerate the softener unit.

Regeneration consists of loading the softener unit with salt to create a strong brine that displaces all of the dissolved elements that have built up in the softener and replaces them with sodium. The remaining brine plus all of the dissolved elements are flushed out through a drainpipe.