They live in an imaginary world where no one ever cleaned glasses until microfiber cloths were widely available.

To clean glasses safely you basically need a soft, clean cloth. Cotton is totally fine. You could get away with a soft clean sponge, too. Or even a soft-ish piece of paper (which is what most disposable lens words are.)

Usually it's not the fabric but trapped dust that scratches the coating when you wipe.

Most believe whatever marketing material or sponsored "expert" advice is presented to them for "proper care", without actually checking. At least glasses clenaning is a harmless area - people do the same for supplements, diets, and all kinds of health advice too.