Permitted? They are US citizens, so they can sign. However, there would be consequences if it was a political hot potato and the DoD wanted to pursue it under Article 88 of the UCMJ. "contemptuous words" can be interpreted many ways.
"Any commissioned officer who uses contemptuous words against the President, the Vice President, Congress, the Secretary of Defense, the Secretary of a military department, the Secretary of Transportation, or the Governor or legislature of any State, Territory, Commonwealth, or possession in which he is on duty or present shall be punished as a court-martial may direct.”