Threading dies are made to do just that - to cut threads. If not careful, you can start removing steel from your threads with them, giving you loose, sloppy threads. Not a big deal if you never use them, but can cause issues if you want to use a silencer on your barrel.
I leave the thread protector on so it can... protect the threads. To keep it from backing off you can either use an appropriately sized rubber O-ring, or wrap the threads a couple times with Teflon plumbers tape.
I’ve been using the plumbers tape trick for a couple decades to keep silencers and thread protectors in place.
