Unless the unsoftened water has excessive metallic taste (iron or manganese), it is far better to use that unsoftened water in brewing. Hard water is ALWAYS preferred and necessary for good brewing performance. Calcium and magnesium are important and necessary ions for brewing, while sodium is not. Alkalinity is not affected by a softener and its this component that is the most important to control. Softened water is counterproductive to good brewing.
If you're brewing with water from the exterior hose bib of a house with a softener, its possible that this water bypasses the softener and you're brewing with unsoftened water anyhow.
Download and read Bru'n Water for more information on brewing water and its treatment.