We obtain sufficient conditions for commutative non-autonomous systems on certain metric spaces (not necessarily compact) to be topologically stable. In particular, we prove that: (i) Every mean equicontinuous, mean expansive system with strong average shadowing property is topologically stable. (ii) Every equicontinuous, recurrently expansive system with eventual shadowing property is topologically stable. (iii) Every equicontinuous, expansive system with shadowing property is topologically stable