Block Property-Based Nonstackable Sorting

Although Nonstackable items cannot be sorted by conventional means, there are several items that have consistent sorting methods. 

The simplest nonstackackable sorters use properties of blocks to whitelist or blacklist certain item types. To sort, items are attempted to be placed in an inventory, and if the item actually enters the inventory, then it is sorted (with the exception of shulker boxes, which are the inversion of this). 

The following is a list of blocks with whitelisting properties, along with the items they can sort using it.

Chiseled Bookshelf - Enchanted books, written books, books (note that written books are 16 stackable and books are 64 stackable) 

Brewing stand - Potions, water bottles

Jukebox - discs (individual discs can be sorted using their signal strength when played in a jukebox)

An Enchanted Book sorter using a chiseled bookshelf.

Note that the bookshelf may be replaced with any of the above blocks.

The slightly different setup required for disc sorting.

There is only only one block that has blacklisting properties: shulker boxes. These can be sorted by utilizing the fact that any item besides shulker boxes can be placed into a shulker box. 

A Shulker Box sorter using the shulker box's blacklisting property.