Why does Newton's 3rd Law not apply to mud?
Newton's third law states that for every action there is an equal and opposite reaction. This is applicable for all bodies.
It is incorrect to say that the third law does not apply to mud. When a person walks on mud, they are exerting force on the mud with their feet. With each step, mud is being pushed backwards. The reaction of this allows the person to move forward. Similarly, if a person were to fall down on mud, their bodies apply a force on the mud. In return, the reactive force applied by the mud is what causes pain and discomfort.
Newton's third law applies to mud in the same way it applies to all other substances. There is nothing that makes mud an exception.