I think I know what you mean, once while I was flying my G.P. Cub 20, an onlooker came over and asked me how it flew. I explained to him with a straight face "Well, with that flat bottom lifting airfoil on the wing, this plane can't be flown upside down because the wing won't lift that way" whilst flying the pattern inverted the whole time I was talking to him. He got the joke BTW.

On aerobatic planes, I like to set the elevator trim for a neutral downline. This makes the plane equally out of trim upright and inverted. I just live with that out of trim condition and actually find that it helps give me a little feel for the plane's airspeed when landing.

It's the CG location that ultimately determines whether the stab lifts, is neutral, or has to make down-lifting force to trim the plane, not the shape of the airfoil.