Piston does not push chests or hoppers

That's because Pistons can't push tile entities at all!
Confirmed!

WAI. Pistons aren't able to push tile entities such as chests, hoppers, etc. The full list of what can / can't be pushed by a piston can be found here: http://minecraft.gamepedia.com/Piston#Pushing_Blocks

@unknown Then why they can be pushed/pulled in bedrock edition?