Description
Right clicking most items on the cutting board while also holding something in your off-hand will put the off-hand item on the cutting board instead of the main hand item. However cakes and wheels of cheese in the main hand will still be prioritized over the off-hand.

Steps to reproduce:
Hold any non-food in your off-hand, and try to place a raw beef from your main hand on the board.

Expected behavior:
It should probably ignore any non-cuttable off-hand items. While having a stack of cuttable items in the off hand, and a knife in your main, and just right-clicking is quite nice for fast cutting, I'd rather it just ignored the off-hand entirely to stop it stealing my shield. If it could still allow cuttable items to be placed via off-hand, that would obviously be the ideal situation.

Screenshots

Mod list:
Playing Enigmatica 6, Forge 36.2.21, FarmersDelight-1.16.5-0.5.4.jar
https://gist.github.com/Rodg88/30b70c6a97a2a8f812bd29a35e6a7eb7

There is a tag for that: farmersdelight:offhand_equipment. Items in it cannot be placed on the Cutting Board from the off-hand.

Chances are the Enigmatica pack hasn't added these shields to this tag (search #offhand_equipment in Creative to check); I recommend suggesting this enhancement to them.

Nice, honestly had no idea this tag existed. Thanks :D