Not sure if the humidifiers being discussed have filters. Here the filter has to be changed every couple of months because of the calcium and Lime buildup.
that ain't too bad. consider flipping it around the cage every week or so. or sunome type of regime. At least you're using humidificaton!
don';t worry about that bad air unless going to far around the bounds
Can you bypass the softener with a Y valve or something like that? From what I've seen softening water removes calcium and magnesium. Maybe just have to amend appropriately (soil or foliar) if you're humidifying with softened water?