When working on fire rated doors can you remove the fire rated tag on the hinge side of the door?

NO. and it cant be painted over either.

If you don't like to see the label, cover it with blue painter's tape cut off the excess tape from the edges and then paint the door and over the tape and leave it in place. If you are asked by a fire marshall to show the rating then peel it off. Reapply if desired.