Stability of impulse response
In this system, the total response is the sum of System A to D.

If you interpret this simply -- A, B and C are stable or marginally stable. D is exponential growth, so it is unstable. (Given D is not exactly canceled by another system) The sum is unstable.

System B and C responses share same roots, the same roots remain when adding them together, just the amplitudes change, regardless how you represent the mathematics (trigonometric or exponential). Notice you are adding and not chaining the two systems together.