I’ve changed in and out of suits in airport restrooms, coffee shop restrooms, in the airplane restroom and in the front, passenger, seat of a 1970s Austin America (r.o.w.: Marina?) while someone else was driving.
Focus. Change shirts, skirts, pants and dresses, and anything under them, in a stall. Stand on your comfy shoes, watch out for wet floors. Look before you commit. Enough paper towels can be carried into the stall and laid on the floor if its icky. Standing at the washroom sinks or other semi-private place risks being immodest, in the opinion of other travelers. But if no-one is there…
Jackets, coats, ties, scarves, hats and shoes can be changed without privacy, socks, if you’re quick.
As several have noted, formal shoes should go on last, come off first. Carry two plastic bags, so the nice shoes don’t scuff each other. Put one in a bag, put that bag and the other shoe in the other bag, at the first opportunity. Switch to comfy socks as you put on each comfy shoe, don’t make a show of your bare feet or the socks you took off. Don’t change socks at your seat on the plane unless no-one else is seated with you.
Keep comfy clothes, some plastic bags and a couple spare hangers in a carry-on suit bag. Make it a small one that’s easy to stow near your seat on the plane.
I used to change socks and underwear at the last hour of intercontinental flights. Refreshing! Especially if you have to a full day of work when you arrive. Start your dirty laundry bag or discard as you wish.