(Tested both on both 1.16.5 and 1.16.4; Forge 36.0.13, and 35.1.37 respectively.)

When adding the forge:all_cheese tag to an item via CraftTweaker, Rats still wont accept it as a tame-able item. However, when adding the tag via a data pack, it works just fine. This doesn't appear to be a CraftTweaker issue, as the tag is definitely getting applied, as can be seen with "/tellme dump to-file ascii-table tags-item" when using the TellMe mod. Also, applying other tags like forge:cheese allows it to be used in this mod's recipes just fine. When CT is used to apply forge:all_cheese, Rats acts like it never happened. In short...

To recreate:
-Add Rats, Craft Tweaker, and TellMe (and optionally simple farming)
-Make a CraftTweaker script with tag:items:forge:all_cheese.add(item:simplefarming:cheese_slice); (or any other item).
testscript.zip
-Load up a world, and attempt to tame a rat with the item used in the script. Notice you cannot tame a rat with the item (and that a /reload doesn't fix it.)
-Do "/tellme dump to-file ascii-table tags-item", and notice that the tag was indeed applied.
-Apply a datapack to the world that adds forge:all_cheese to the same item(the datapack I used is attached), and /reload.
testdatapack.zip
-Attempt again to tame the rat with the same item. Notice everything is working as intended.

The rats cheese tag now follows the same convention other mods use for their cheese now, so this shouldnt be an issue anymore. All items tagged as forge:cheeses will work for taming rats. If you want to add more items to this tag I highly recommend using a datapack instead of crafttweaker, although using crafttweaker should be just fine