Key and ID should always go on your body. If there's an accident or incident you and your bike may be separated. Especially if the cyclist has a concussion. Some friends have had that unpleasant experience. So I don't keep my door key or ID in my seat bag.
A key, ID and emergency contact/insurance info don't take up much room or weight. A flat, waterproof wallet could be tucked inside the jersey, even with a skinsuit -- probably easier to reach from behind if it's a rear-zip skinsuit.
With bibs I usually use a small Velcro strap to attach my door key around a suspender. I don't notice it during a ride. I don't have a skinsuit, just a couple of aero jerseys with minimalist pockets. My mini-wallet with ID, VA health card and a $20 bill fit in the middle pocket along with a couple of gels, no problems.
And I tuck empty gel wrappers inside the hem of a bibs/shorts leg. Never even notice during the rest of the ride. I'd tuck a key and ID there too if it was secure but it'd fall out without a sort of pocket.
Heck, even a skinsuit should include a tiny pocket on the back for a key and ID. Can't imagine it would upset the aerodynamics much, if at all. Wind tunnel tests show some oddities, such as race numbers flapping around sometimes helping rather than hindering airflow over a rider.