The trick to making peace between the Iconoclasts and the MSI is to always do and side with Zora Blackwood whenever you have to make a choice.
The Iconoclasts' own sub-story line begins with Graham and Zora asking you to retrieve the cartridges for Graham, or the food and medicine for Zora from the MSI supplier Carlotta. This leads to an outpost where Carlotta is locked behind a door and has to be talked to through an intercom in order to open the door.
When Carlotta opens the door, she will ask what kind of supplies you want. It is imperative to pick the food and medicine supplies otherwise there will be no way to make peace between the Iconoclasts and the MSI down the sub-story line. Similarly, during the "Starting the Press" quest, make sure to retrieve and talk to the Zora's men. They will require you to retrieve some medical kit in order to be able to fall back to the Iconoclasts' base.
Long story short, these two decisions will later on make Zora want to talk and she will offer up a quest ("Sucker Bait") that, when completed, will eventually lead to Zora becoming the leader of the Iconoclasts and she will also agree to make peace with Sanjar and the MSI.
Essentially, the peace outcome is conditioned by requesting the food and medicine supplies from Carlotta and talking with Zora's men outside the press. If any of these two are skipped, Zora will either not want to talk at all, or after suggesting peace to Sanjar and coming back to her, she will complain that you are too goal-oriented, much like Graham, and will eventually lead you to having to buther one or the other faction.
A repeated design flaw in RPGs, in general, when a huge outcome hinges on some brief dialog option or minor action (TL;DR, in the end, Carlotta was not discovered, she could have delivered the cartridges too, there is no notion of "time" that affects the linearity of the game, Zora was already at odds with Graham, etc…).