Yeah, I've seen threads from the poly tarps in nests - I don't think it's as much of an issue as it would be if they were eating them? And the stuff you're getting in the dryer has just been washed, so then only problem would be dryer sheets, I'd guess. Maybe just the lint from drying rags.
And all of that stuff goes into my compost bin, too, so I guess I can do a "one for you, one for me".....