Affected by previous and current Minecraft versions. Single chests have inside texture on lid and vice versa, double chests are not affected. I reinstalled Minecraft but the issue was only solved for about a day. It came back when I entered a Survival Mode world and affects all worlds of mine. I have no mods installed and the texture pack isn't causing it.
I was wrong, it was an outdated resource pack causing the issue. Although I had checked it wasn't the cause, I must have missed something.