Is it rude for a deaf person to talk sign with their mouth full of food?

Yes, I think so, because during sign conversation you are also reading facial cues, as you do when someone is speaking. It's probably better for them not to be chewing food at the same time.

Answer

No, it is only rude to sign with your hands full. Of course opening your mouth while it is full is rude regardless of whether you are speaking or signing.