My Grandmothers, my mother, my MIL and I all padded ironing boards with whatever worn cotton goods we had at hand. Of course our ironing boards were/are really boards and so we could tack on padding: bed spreads, flannel, drapes, mattress pad sides, etc and topped with an old percale sheet, worn to silky smoothness.
I recently had to strip all the layers from GMIL's board (Dpuppy peed on it). I was able to wash/bleach and re-use 80% of the old padding which was at least 60 years old.
As long as you avoid synthetics/vinyl/rubber use what you have.