Source? Not sure how much vinegar is too much, not a chemist, but I add a splash and here is why. Citric acid is used in the cosmetics industry to soften water and acetic acid (vinegar) should be no different. Hard water is more alkaline (basic) than soft water, so it would be softened by adding an acid. The mechanism is by the acid neutralizing positive calcium ions. https://www.aquatell.ca/blogs/aquatell/does-vinegar-soften-water

Baking soda makes water feel slicker, because sodium bicarbonate is a surfactant. Washing soda (sodium carbonate) does remove temporary and permanent hardness by precipitating magnesium and calcium, taking these ions out of solution.

Keywords to google: temporary hardness, permanent hardness, washing soda