One who is classified as an Ivich Supporter is slightly beyond just being Neutral. An Ivich Supporter believes in what the Ivichs are doing is right and they would rather see them win, not the Venkons. An Ivich Supporter does not get involved in the war, but acts as moral support for the Ivichi side.
The difference between Neutral and Ivich Supporter is the fact that someone who is completely Neutral shows no support in either side, will not get involved, but may/may not take interest in the war itself. An Ivich Supporter will not fight, but will support the Ivichs in hopes of their victory.