For what reasons would you support forbidding disloyal language about the military during wartime? for the reasons would you object to such a law?

One of the main reasons for this is in order to stop losing support for the war effort. As was seen in the espionage act and the sedition act, talking disloyally about the war effort was seen as treason and people would be punished for such things. This was because the government did not want the people to sabotage the effort and to prevent others from supporting the war effort. 

You should object to such laws because they infringe on first amendment rights since they are limiting your freedom of speech. Thanks to supreme court action, such laws would not be passed today because they would be unconstitutional since people have the right to criticize their government in a democratic country.