I just upgraded to the new version of Minecraft for the Xbox and noticed this problem. It's a difference between the way the Xbox One Edition used to function and the way the Xbox Live version functions now.

We used to be able to put a half block or on top of a chest and it would still open.

Many people have done this in their chest room designs so they can stack chests all the way to the ceiling, but the ceiling was nice and uniform above the chests. People have also used upside down stairs to create a wall directly above chests, but allowing them to still open.

Converting my world from the previous version of Minecraft for the Xbox into the new version of Minecraft for the Xbox, broke this functionality on many of my chests.

Upside down stairs still work, but half-blocks don't.