Dissenting view here.
I detest microfiber towels in diapers. I don't like the way they feel on my skin. I don't like to fold them, I don't like the way the colors show through my pockets, I don't like how spongy they feel when they are wet. I don't like the way they pick up lint and stick to everything in the dryer. Velcro comes to mind.
I LOVE natural fibers. I love how organic cotton feels. I haven't had a problem with trimness or absorbancy with my cotton fitteds or hemp inserts. Natural fibers make me feel good. I want diapering to be as happy for me as I can, so no cheap microfiber towels in my diaper stash.
I do want to be fair to the poor towels though. I use the microfiber towels that I originally purchased for diapering as cleaning cloths. I also have several much nicer microfiber towels that I use for camping. I *might* consider the nice microfiber for diaper inserts, but I love it too much as towels.
It's a personal choice thing, IMO.