For starters, I think that you innately misapprehend he meaning of “neutral”. Several people seem to be.
“Neutral” does not mean “does not fight”. That’s a pacifist, or someone sworn to nonviolence.
From the dictionary: “not helping either side in a conflict, Disagreement, etc.; impartial”.
When two people or countries are fighting, she doesn’t help either. That’s does not mean that the Archive does not pursue its own purpose. It means it doesn’t help others with theirs.
Look at the example of McAnally. He is neutral, “out”, however you want to say it. And yet when an entity invaded his personal territory, he is free to defend that territory. That doesn’t make him “not neutral”. Nor does it when he helps a groggy Andi. He is still stubbornly neutral.
From the perspective of the Archive, the human race, this world are her territory, and she is doing nothing but defending it against threats. Not taking any side but her own.
The Archive is pursuing her own purpose in eliminating the threat of various monsters. She uses her minions, regardless of their other affiliations, to do so. She’s neutral. She doesn’t help anyone fight their wars, she only fights her own.
Please don’t confuse “neutral” with “inactive”. They aren’t the same thing.
How does this make her any different than Marcone or "any other of a dozen neutral arbiters under the Accords?" Is Marcone also therefor bound by neutrality? Ivy might be neutral in the most dry, technical, legal sense, but in any practical sense of the word, Ivy is likely rarely neutral.
I would grant that the Archive could be largely neutral in a conflict between two targets of obliviation, unless she was the instigator of the conflict in the first place. I would also offer that she would take advantage of the weaknesses such a conflict would present to advance her agenda of obliviation. She probably wouldn't ever be totally neutral.
A good example of this the the White Council's war with the Red Court. Ivy ended it.
If not for Ivy, Harry would not have approached Vadderung. If Harry had not met Vadderung, he wouldn't have known to go to Chichen Itza. (Except that this is a fictional story that Jim would have worked out differently). The point is that Ivy took sides in a supernatural conflict to decisively end it in favor of one of the participants.
Ivy is a participant in the larger and ongoing conflict for power in the supper natural world with her own agenda. She may be neutral in this or that conflict, but the White Council and the Faerie Courts are also often neutral in a particular conflict. It doesn't mean that any of them are inherently neutral. I wouldn't be surprised is Ivy is never truly neutral in any conflict. I would expect the Archive to be constantly pushing things this way or that way. I think "undeclared" would be a much better descriptor of what the Archive is actually doing than neutral.
Further, we don't know the extent of the Oblivion War. Is Ivy trying to eliminate everything that is supernatural? The White God, wizards, minor practitioners? Is she only targeting certain supernaturals that prey upon humanity? If it's the latter, she will never be close to neutral in any but the narrowest sense of the word.
And the Archive is certainly not bound to neutrality, which was my original point. Arguing that examples of the Archive being neutral doesn't in any way mean that the Archive is bound by neutrality has convinced me that the Archive is seldom even being neutral. The Archive is, at most, bound to the appearance of neutrality.
in Small Favor Luccio warns Harry that the Host still has control over the Archive. Normally by the time the female candidate inherits the Archive she has had a life time of
emotional experience to insulate her from all the lifetimes of the Archive Hosts. Ivy hasn't had any of that, she has just been distant until Harry came along, and to some extent Kincaid both attempting to treat her like a normal kid which she has never been.
Luccio asks the question page 408
Luccio is speculating in that conversation. She states that the many well known oracles were actually the Archive. These oracles helped sides in conflicts. They didn't meet the dictionary definition of neutral. If the Archive is neutral, Luccio is wrong that these women were the Archive. If she is correct, the Archive isn't neutral. If the Archive isn't neutral, Luccio is wrong about the Archive.