Considering that the organization is primarily a union between elves and humans, I'd imagine that the Kirin'Tor distance themselves from the Alliance and Horde to prevent the split of their city. Most of the high elves in the world joined the sin'dorei, after all (this can even be seen when Kael'thas, who was a member of the Kirin'Tor and was in Dalaran at the time of the sacking of Silvermoon, left Dalaran and renamed his people "Blood Elves." Chances are that many elves who were in Dalaran were sympathetic towards their prince and shared his sentiments if they didn't accompany him directly).

You can sort of see the start of this polarization of the Kirin'Tor in Wrath of the Lich King. I'd imagine that when the Scourge War and Nexus War ended, the Kirin'Tor devoted themselves to realigning the world's ley lines after Malygos uprooted them, and that would require ALL of the Kirin'Tor to remain united. So it's probably an issue that Rhonin and the rest of the Council has swept to the side. For now.