Always clamp the post, dropper or not, carbon or not, aero or not. The only time I don't is if there's no seat post installed. Then I set the jaws horizontal and use the top tube, but don't really clamp, and I don't do a lot of force (e.g. taking a BB out). Mainly to get a seatpost in, then move the clamp to the seatpost.
Just wipe the jaws and dropper first before clamping.
I think it was Park that did a video on how it's totally OK to clamp the dropper, and any forces while wrenching are way less than your body puts on the dropper.