Pillowcases yes. Back in the sixties used to put brown paper over my hair on the. Ironing board and iron my hair. No ghds in those days. One day tried without the paper. Large chunk of hair went the way of whartons knickers.
I'm such a disappointment to my mother, she irons everything - I don't even pick up an iron these days (arthritis) but I do insist the "staff" press the pillowcases
I iron nothing accept a linen shirt I wear onc ein a while - I shake the washing before it goes on the line and again when I unpeg it. If its folded immediately and smoothed flat it never needs ironing.
I iron just the duvet cover and the pillow cases. I have a tumble dryer so to get rid of the creases I make sure I put sheets back on the bed while they are still warm (my mother would be horrified "What? not aired for 2 days? :)