When using a Data Pack that changes which items are considered "dyeable" (changing the color by combining it with one or more dyes in a crafting grid), the resulting item has the correct "dyed" data value just as Leather Armor/Leather Horse Armor would, but the item cannot be "washed" (removing the "dyed" data) by using it on a Cauldron containing water like the others. 

To reproduce;

• create a Data Pack where data>minecraft>tags>items>dyeables.json reads:

{
    "replace": false,
    "values": [
      "minecraft:stick"
    ]  
} 

• add it to a world and reload.
• dye a Stick.
• attempt to wash the dyed Stick in a Cauldron with water in it.

(Changing the "replace" value in dyeables.json to true, effectively removes Leather Armor/Leather Horse Armor from the tag, and any that were dyed prior to reloading the pack can no longer be washed. This indicates this is expected behaviour, not a "feature request" - that items included in the "dyeable" tag should be washable.)

Potential solutions:

• remove the hard-coded arbitrary check for Leather Helmet/Chestplate/Leggings/Boots/Horse Armour when attempting to dye an item and just use the "dyeable" tag, instead of using both.
• ignore "dyeable" tag completely and let any item with "dyed" data be washed