I usually hand wash mine, but have tossed them in the washing machine a time or two, without incident.
Isn’t the cloth that comes with Rics treated with Zymol or some kind of polish or cleaner. Mine certainly smells like it is. Unless you’ve had it for a while and the treatment has worn off, I wouldn’t wash it.
I probably should have specified that I was referring to microfiber cloths in general that I own. But yes, if treated, I wouldn't wash either.