White Stains Appearing?

I have started having white marks/stains on all my dark colored polyester pants and most tops. The marks are all over the clothes; back, sleeves, etc. (not underarm). They look similar to the white stains you see from salt on things during the winter (except they aren't powdery like that) or a little like burns from an iron (although not shiny). I thought they might be from my dryer sheets so I tried using liquid fabric softener tonight, but they were still there after the clothes dried.

The only way I have been able to get rid of them, temporarily, so I can wear the clothes, is to use the kind of stain remover that you spray on, blot with a cloth, and don't wash off. But, after I wash the clothes again, the marks come back.

I use liquid detergent (All) and a cap of liquid Calgon for hard water. I usually use dryer sheets. This has become very frustrating and I joined here in hopes that someone in this community might have an idea of what I could do to fix this problem permanently.

Thanks!
Laurel from Kokomo, IN