Commercial liquid soap can have all sorts of additives to make you feel moisturized, while the opposite actually is happening. I have very dry hands. Not now, but that have been a problem my whole life. And I have used commercial liquid soaps. When I switched to homemade bar soaps, my hands healed. I can still be slightly dry sometimes, but not as much as I start to bleed. And bleeding hands were more or less the normal condition before. I don't have to use all sorts of remedies anymore for dry hands. Nothing.
The point is that my handmade soaps feel much more cleansing compared to many liquid soaps. But, they are the opposite, they are way less stripping than any liquid soap I have used. Something I can see very clearly just by looking at my hands. So squeeky clean is not necessary a bad thing, as long as your soaps are not drying to your skin. The oily moisturizing feel of commercial soaps are nothing more than an illusion. They will dry you out more than handmade bar soaps. But we have all different skin and react different to different things, so it might be the opposite for some.
If your soaps make you squeeky clean AND dries out your skin, well, then you have to look at your recipe. Adding a chelating agent, as several suggest, that is really something you should do. Soap scum will dry out your skin, and you have hard water, so you definately need a chelator. I use citric acid (to make the chelator sodium citrate) and I have soft water. I use it primarily to prevent DOS, but also to reduce soap scum (which is not a very big problem in soft water, but it is some, I think).
