Most fabric softeners are nothing more than emulsions of waxes, oils,surfactants and water designed to coat fabrics. This coating smoothes fibers and also allows them to "untangle" and "fluff", and also stop static cling which is why terry cloth towels, as well as your hair feel nice.
Cationic (sp? too tired to look it up), surfactants are the main actors here, and these chemicals are found in all fabric softeners, and hair conditioners.
To the best of my knowledge fabric softeners as will soap added to a detergent wash will control suds, but the detergent is still there. By reducing sudsing in theory it should be eaiser to rinse the detergent away, but cannot imagine that oils, waxes and such have any effect on removing alkaline substances (which what most powdered detergents are).
Now vinegar will remove alkaline residue because it is a mild acid. Thus adding vinegar to rinse water will help remove remaining detergent and bring the pH level down thus ensuring a more skin friendly final result. Laundries add acid rinses "sours" to remove excess detergent/alkalinity and bring the pH level down, but only to wash loads done with powdered detergents. Commercial powdered detergents usually have been quite alkaline, because a high pH breaks down oils/soils , which is why Fels, brown, and lye soaps work so well. But with the use of enzymes and other chemicals powdered detergents have come down in pH level. Liquid detergents are almost always neutral to slighly acidic thus do not require "souring", which is why many commercial laundries have switched to them, as it saves steps and money (one less chemical to purchase).
Vinegar and salt have no effect on modern dyes. Ages ago when dyes were made differently both vinegar and sale did work to an extent which is where the tradition grew. Have vintage house keeping books from the 1920's and 1930's which suggest adding one or the other substance to prevent colours from bleeding. Mind you if laundering a vintage item, do give either a try. Was laundering a vintage red table cloth that ran like the devil, but a splash of vinegar in the water stopped the color cold.
By the way German Persil contains small amounts of soap for just the reason sited above; it controls suds and aids in rinsing. Silicone (an other type of oil), also does the same thing.
Launderesss