This is interesting thread from the point of the refs in here.
IMHO, I think the main responsibility of the ref is to keep the players safe. Everything else comes after this.
I think it is also interesting that the refs won't physically engage the players. I'm not sure how I feel about this, honestly. I see the point of not touching kids, because of all the issues that can come up.
Having done some refereeing in the AYSO, I would probably make an attempt to physically separate 2 actively fighting players. If one kid is pummeling another kid, do you just stand there watching (or blowing your whistle?!). I think there must be a line where you intervene for the safety of players. But probably 99% of fights end quickly without you having to jump in there.
If you look at NFL, NBA games-- those refs will get between players and touch fighting players. Now, these are adults, so maybe that is a difference. But I don't think I could just watch 2 kids fighting without doing something beyond blowing a whistle.