Thoreau says that soldiers are on the same level as wood, earth, and stones because they blindly do what the government tells them to do. When they do that (rather than paying attention to their own consciences) they are no longer like people.
To the transcendentalists, it was very important for people to follow their own thoughts and their own consciences. For example, Emerson (who was a transcendentalist like Thoreau) said that "whoso would be a man must be a nonconformist." Thoreau is saying the same thing here. He is saying that anyone who just blindly conforms and does what he is told is no longer a man.