...I wash my cast iron with warm soapy water. Cringe if you must, but here's my explanation as to why I do what I do. First and foremost comes food safety. Residual animal fats at room temperature (red meats, poultry, seafood, butter, etc.) do not make for good eating. Next, using warm soapy water with a soft cloth or sponge is a good way to get all the leftover loose bits out of the pan without much of a mess. Since I was a kid, my grandmother used a cast iron skillet for most cooking tasks. That pan (sans handle) is still black as night and smooth as glass and after every use gets washed with the rest of the dishes.
To allay some of those cringes, I do not scrub, only swish and rinse. Since the cookware is properly seasoned, nothing sticks. After the bath and thorough rinse, I dry the pan with lint-free towels and place it in close proximity to my cooktop's pilot where the warmth can complete the drying. Finally, before returning the pan to its parking space, I place a couple of drops of veg or olive oil inside the pan and give it a nice rubdown while its warm. Once the oil is spread neatly and everything is covered, I take another piece of lint-free towel and wipe out the excess oil so things don't get sticky.
My relatively new (in chronological comparison to my grandmothers') pan is shiny and slick although the blackening is a work in progress. Matter of fact, I made some cottage fries earlier this afternoon and they crisped up so nicely compared to those non-stick jobs and nothing got stuck. Awesome! I haven't tried proteins yet, since I just restored the pan after a long-term stint in poor storage. I do have a Cornish hen thawing in the fridge and I think this pan might get a go as a baking tool to see how things work out.