What I expected to happen was...

Contents of chests should be unchanged after update.

What actually happened was...

In some (not all) chests, the top 3 rows are swapped with the bottom 3 rows. All items seem to be present but are rearranged.

I do not know how to predict which chests will be affected. I do know:

It happens with trapped chests as well as regular chests.

In a bank of stacked chests, some entire columns are affected; in other columns, only some are affected.

Unstacked chests are also affected, both ones with neighboring chests and ones separated from other chests (again, only some chests, not all).

It affects both north-south and east-west oriented chests.

It affects both singleplayer and multiplayer worlds.

If copies of the same world are updated, the same chests seem to be affected each time.

I see that this was reported in 1.13 pre-releases and was "resolved" as "will not fix". But it is still happening in the 1.13 full release. 

Steps to Reproduce:
1. Create a world in 1.12
2. Set down several double chests and put items in them
3. Re-open world in 1.13 and check the chests