they might have a soap residue.
If you haven't already done it, give the washer a service wash (no powder, no fabsoft, a cup of washing soda, the hottest longest wash it will do. If the water goes grey and foamy with old soap, do it again until the water stays clean)
Then put the towels in, no soap, no fabsoft, half a cup of washing soda, on a cotton wash (if they are coloured they are more likely to fade from the very hottest, longest wash; but OK if they are white). Again, if the water goes grey and/or foams up, that will be old soap residue coming out. Do it again until the water stays clean.
Cool washes do tend to leave more residue as the soap does not dissolve so well.
If you find this helps, buy a bag of soda crystals and use half a cup per wash for a week or two, see if it suits you. They are not needed if the water is soft.