I'm puzzled about which poly messes up with a hot iron. I've sewed I don't know how many shirts, tops, nightgowns out of polycotton broadcloth and batiste. I've used the hottest steam and never had a problem. I think the mix on those is 65/35 or it was. It always had more cotton than poly. I also use a blended permapressed muslin.
The old doubleknit might have made a mess. That stuff was just plain awful and a cat hair magnet.
Lycra never got pressed or ironed.