I guess there's some synthetic in my whites, including underwear and socks but I haven't noticed problems. Still, it's a consideration.
Thing about drying outdoors, if conditions are decent and you leave it out there long enough and in a breeze (it's usually pretty breezy here), you know it's pretty dry. With a dryer unless you leave it in there a long time, you can't be sure. And there's the noise! I'm not even sure exactly how my dryer works. I bought washer and dryer off a couple acquaintances used and have never been able to find instructions. Sears Kenmore stuff, pretty old now. It's got dials, timer, it works but I don't know the ins and outs.