I have never heard of that, there isnt much logic to it. First there are huge variations in microfiber rags, some would be more abrasive on plastic (coated monitors) and should not be used on them to begin with. Some microfiber rags do not have fibers sticking upright (like terrycloth). This type of rag might more commonly be sold for that purpose. A good "polishing" quality microfiber rag works great.
Any rag used on anything would collect particulates, dust, any dirt and all. If there was going to be a problem it will exist when collected things exist (not clean). Leaving it out collecting things falling down all around. Multiple cleanings of dusty surfaces engraining in the fabrics other particals and materials.
I wash mine all the time, with one problem being washing powders and liquids, most of them even hyperalergenic and other cute names, will leave a residue on what your washing, this residue is to make things appear cleaner, or feel soft, that residue then can cause smearing, and might also be more likely to hold dust and dirt. I Prefer to use a non fragrance dishwashing liquid (dawn original) in small quantities (foaming), and not to use any dryer sheets of any kind.
Can they be reused without problem? what would change? it is just a plastic fiber cloth item, they are not rounding off things, it is just woven (or whatever they would call that), same sized fibers. Yea they can be re-used, the things I outlined would be the bigger problems.