No. Don’t worry, it will not hurt them. I remember the concern was over age and that the integrity of the info on disks was supposed to be only something like twenty years. I have CDs going back forty years without a problem.
My CDs like my vinyl no longer gets played since streaming now sounds as good or better, cost a fraction, and gives access to over ten million albums. They look nice covering my walls. Don’t forget to consider streaming before investing in any more physical media.