That "slick feeling" indicates that all the soap IS being rinsed off the body. When the water doesn't feel slick, it means you have soap residue/scum still on the skin. So you truly want the slick feel. That means you're really clean.
That is what the water softener sales websites say. Imagine what would happen to their sales if they said that slippery feeling was soap that won't rinse off.
Here's the truth about it.
Soap removes oils. That's its main function and "raison d'etre". The soap molecule, made long ago by reacting fats with lye (NaOH), has the inorganic Na cation at one end of the molecule. The other end is organic, derived from the fat. And the way soap works is that the fatty end of the soap molecule attaches itself to any oils on what is being washed, and it pulls the oils away when the soap is rinsed away. Soap also attaches in the same way to amino acids, which is the stuff of skin. But while pure (softened) water pulls away the soap molecules that are attached to oils, taking the oils with it to rinse down the drain, water is not very good at pulling soap away that is attached to the skin's amino acids because the soap molecule is more strongly attached to the amino acids than it is to the water molecule. So with "pure" (soft) water, soap is left behind, attached to the skin's amino acids while oils are washed away. And therefore, with soft water the skin feels slippery, and the slippery feeling is the soap that is left behind.
Hard water helps with this problem. It has hard-to-dissolve calcium compounds in it and those calcium compounds, being inorganic, attach well to the cation end of soap molecules. So a water-to-calcium-to-cation-to-soap-to-amino acid chain formed, and the water pulls on that chain and breaks the soap-amino acid bond and rinses the soap away, leaving "squeeky-clean" skin.
So the problem is how to have soft water for its benefits, but also get the soap off the skin and eliminate that slippery feeling. And the solution is to substitute another inorganic compound for the calcium that the water softener removed from the water. What's needed is a compound that will form a good bond with the soap cation, but will not leave scale and produce the other problems of hard water. One compound that works quite well is Epsom Salt. Just get a 5-10 ounce spray bottle, fill it with hot water, add a half teaspoon of Epsom Salt to the water in the spray bottle, mix, and take it into the shower with you. After bathing and rinsing, spray some Epsom Salt solution on your skin, or on your hand, and rub it over the slippery areas of your skin. You'll feel the slippery quality diminishing and being eliminated as the Epson Salt attaches to the soap film (which in just one molecule thick) and rinses it away. Then rinse the Epsom Salt off with the softened water from the tap. And the bonus is that your doctor will tell you that Epsom Salt is good for your skin.
If the slippery feeling was "clean skin", the Epsom Salt would change nothing; the skin would remain slippery. But it doesn't because the Epsom Salt removes the soap that remains stuck to the skin.
Yeah I know this thread is 18 years old. But this remains a controversy due to water softener propaganda.