At the washing machine it should still be passing through the softener. Usually they Bye Pass for exterior hose bibs.

As far as whether to go W/ R/O ? Personally I'd opt for the Bye Pass, but that depends a great deal on your local water quality, and how well you get along with your HOA ??? R/O has it's own inherrent issues to deal with. A high quality industrial water battery will pretty much remove everything, and then you have to reassemble the water as you see fit. This can get tedious as well. We have 4 different sources here all intended for point of service.
Straight tap, Softened, Solid carbon/ceramic matrix, and an Industrial Battery W/DI and, dual R/O. Chemically pure water is actually kind'a Caustic/Corrosive since it is lacking in any or all hardness it's a little hard on stomach lining !