Hey I came across this searching for the answer to this exact question.
Which I think is NOT about incorrectly hemmed items where basically the fabric is not folded perpendicularly. Or it shrinks and distorts, so what was perpendicular before, is no longer so.
I have been fighting these creases in the middle of cotton tablecloths, napkins, kitchen towels etc. They are usually not just a crease that keeps coming back in each wash, there is often discoloration as well; the crease tends to be lighter.
Ages ago I heard (in apparel design class) that this has something to do with the chemicals and dyes applied to the fabric. There is always some residue that did not bind to the fibers. When you first wash the fabric, and it inevitably creases in the washer, those chemicals pile up or get washed off or something like that unevenly at the fold. Some also bind finally, especially in high temperature water. And those are permanent changes that you cannot undo with an iron.
I think there is a case to be made that hand washing these kinds of fabrics initially in cold water and maybe even with one of those special detergents that remove dye residue should help. I never tried this, but started wondering and looking on the internet because I really don’t want to mess up a new tablecloth I just got.
Anyway, just some morsels that may be helpful.
P.S. I always hang to dry and iron my tablecloths and napkins, (even my bedding sometimes). That does not solve the problem.
