In my humble opinion, before I see any other replies, I would say yes.
As one who served in the Navy for nine years, I came to understand that the military function is to serve the people of the nation, through the agency of the current government and with the Head of State as one's focus for loyalty and duty.
If circumstances change such that the serving member cannot give his/her full, undivided loyalty to that Head of State (whom one assumes is in that Office with the agreement of the People), then the serving member must get out of the military. Then, and only then, is he/she in a valid position to criticize.
Open to other opinions on this.