Why are my white sheets getting thin 3" long stains from the dryer?

I hope you can help. When wet, white and light colored clothes go in to my dryer, they come out dry with random skinny 3" long rust-colored stains on them. My guess is that ALL my clothes are being stained but I only notice on the light colored clothes and light sheets.

What can I do to fix this? I like the large capacity of my dryer and I don't have the room for the new larger machines. The dryer is stacked on top of my washer. Would it make sense to replace the drum AND the felt, bushings etc?

Thank you!