Calgon liquid is mainly sodium citrate, and Calgon powder sodium carbonate and other water softeners, but no phosphates.
Laundry at least that worn close to the body and or soiled with bodily fluids like sweat is acidic, not alkaline. Most if not all body fluids; sweat, tears, urine, even blood are slighly acidic. For one thing it helps provide a hostile environment for germs. However if left sitting for along time on laundry, sweat will turn alkaline. This why one is advised to use ammonina or alkaline substance on fresh sweat stains, and vinegar on old ones.
Soap is deactivated in the presence of acids, this includes the acids coming from soiled laundry. Housewives would combat this by simply adding enough soap until they had suds that would "stand up".
Have many vintage laundry books from the 1930's and 1940's, where both STPP, TSP, washing soda, and borax are discussed for softening water. So phosphates must have been around back then, probably easy to find at local chemists or general store.
Yes, pure soap is not great for laundering in cold water, but Fels and the any other "naphtha" containing soaps were excellent for laundering in all water temps. It was the petrol that did most of the cleaning, rather than relying simply upon pure soap. Even as late as the 1940's or 1950's hot water on demand from a heater was not something every housewife had; these ladies had to resort on wash days to the same methods as their mothers and grandmothers, boiling kegs of hot water.
Fels soap by the 1940's was more a "detergent" than soap. It contained fabric whiteners, water softening agents, naptha, and other chemicals that made it a great "heavy duty" wash product. However like all soaps, Fels suffers from one major drawback, soaps do not totally rinse out of laundry. Even with several warm rinses, a tiny bit of the oils/fats to make any soap remain. Eventually this soap residue will cause fabrics to grey, and even smell. Instant Fels, was advertised as having "built in fabric softeners" which really was nothing more than the left over fats/oils from the soap.
L.