To clarify, I'm not talking about any laws that would prohibit people from sharing classified information, but rather publicly questioning the morals of their respective government or the course the war is taking. In Germany speaking out against the regime or the war effort was harshly punished as was the case with the White Rose resistance group. So I'm wondering, have there been any similar cases within other parties of the war, specifically the western allies?
In the USA there was an Office of Censorship which had a censorship code of prohibited topics. They pertained to information that might be classified or beneficial to the enemy, or harmful to the war effort (non-classified information, like rumors or repeating of enemy propaganda, could fall into this category). They did not to my knowledge include morale-related discussions. And they were voluntary in the sense that they were not legally enforced, but it was a matter of patriotism, cooperation, etc.
To my knowledge there were not government-enforced codes that affected political speech in the USA during WWII. That is not the same thing as saying that everything was "fair game," since appeals to patriotism, etc., could still be a strong force. But it is not a situation like World War I, where the Espionage Act was used to imprison newspaper publishers who advocated against the war, and it was not like Germany where harsh punishments awaited any criticism of the regime.