In high humidity, some water will condense on the surfaces of a glass rod and a fur, which may affect their triboelectric properties. As a result, when they are rubbed against each other, the charging may not be as effective. In this scenario, the water does not neutralize the rod, but just prevents it from being effectively charged in the first place.
Let's consider a different scenario, when you charge the rod in a dry room and then move it to a humid room. First, some water will condense on the surface of the rod. If the condensation level is high enough, the water may form a continuous layer and, by dissolving some minerals present on the surface of the rod, become slightly conductive. In this case, the charge will flow off the rod into your body and, thus, effectively, neutralize the rod.