The water softener is a replacement process in which calcium ion is replaced with sodium and the calcium removed and left on the zeolites of the softener.

So what you have in softened water is “salty” water due to the replacement of sodium for the calcium ion. You are experiencing on your humidifier pads “salt” plus traces of calcium and iron.

Yes, indeed you can get a small water softener that is entirely different in operation that would be suitable for your humidifier water supply. That is called a “reverse osmosis” water softener. It is a “filter type” that takes well water as is from the well and filters out those water molecules containing the calcium ion, they are larger than pure water, flusing those down the sewer and allowing the so call “clean” or calcium free or pure water to pass into a jug for you. Clean water molecules comprise about 10% of a well’s output. So there are many in the supply that are “clean” and pure. This is the process used in Grocery stores. They take ordinary water and filter it using “reverse osmosis”

You can buy a reverse osmosis small system from several sources for about $150 . Check these out under “filtering systems, reverse osmosis” on the Web’ s Google Search.