A moderate is a character who can look at the situation without biased or extreme viewpoints and come out with a viewpoint that can be on one side for completely valid reasons.
Take Greagoir for instance, he is an experienced and long serving Knight-Commander who runs his branch with a firm, yet fair hand. He doesn't have an personal malice against mages and views their magic as both a gift and curse. He understands and accepts the full danger that unchecked magic can have on the general populace and serves the order to protect said populace. Yet, he won't pursue mages without just cause, will call off the Right of Annullment once Uldred's rebellion is put down, and has a grudging respect for some mages such as Irving, Wynne and any other mage who controls and uses their power responsibly.
But moderation in a conflict like the Mage-Templar Conflict is probably very difficult considering how that war is a symptom of many layers of inherent problems with the Circle System and the Chantry itself. There may not even be room for a moderate who hasn't been persuaded to throw all in for one side or another. Even Vivienne, a mage who opposes the mage rebelliion, appears to be a pro-chantry mage which makes her very likely to sympathize with templars.