The regular cage and the hopper cage do not accept the hay bale block. Regular clicking and shift-clicking make no difference. Instead, the hay bale is placed as a block next to the cage.

This has been tested in 1.16.3 with Forge 34.1.25 using the mod version 1.2.3 and no other mods installed.

I am also having this issue. 1.16.3 and Forge 34.1.42

mods.txt
Here is my mods list

I was testing new environments and I accidentally changed hay bale into grass block in the recipe. It will change back into hay bale in next version.

Should be fixed in 1.2.4. If not create a new issue.

I had a chance to test it today. Working great!