I've fully completed the Stormcloak civil wars. Now normally I would see Stormcloak guard in every hold but for some reason I still see the Whiterun Guards patrolling Whiterun.

Does anyone know why or how I can fix this?. I play on Xbox as well so I'm unable to use console commands.

Maybe they switched sides to the 'Cloaks, but never got their new uniforms?

Seriously though, I know what you mean. It is like the immortal legates in all the Imperial camps. Bethesda did not clean up everything after the CW ends.