The Vatican's secret service (yes it was in oTorg): they are the secret arm of the "Congregatio pro doctrina fidei" the official successor to the holy inquisition and are investigating all rumors of miracles and magic. In addition they are sponsoring secret missions against the cyberpapacy
National security agencies, though technically all Core Earth security agencies work together via the Delphi Council, each nation, of course will have its own agenda and most are planning for the time after the war. Some may think it could be possible to win the war, some may play it safe and hope the invaders won't notice them, some might even secretly help the invaders in the hopes the invaders might be grateful for that. In addition different agencies even from the same country, traditionally distrust each other. And there is also the issue of former enemies that will never work together even in the face of the possibility wars. I can't imagine the Mossad and the PLO working together even against Mobius.
Big companies also have their own security department. Faced with the possibility wars they can easily become a real security agency (yes, we are deep in Shadowrun territory here)
Soldiers of fortune organisations aka private security companies like executive outcome or blackwater surely will find new opportunities in this world-wide war.
Mafia organisations are basically companies centered around a secret army. They could find work on both sides of the war or realize they could lose everything they ever had if they don't fight for Core Earth
And of course, if a GM wants the Delphi Council to be the bad guy at least for the players, you can always take a clue from A-Team or Burn Notice. Though the organisation itself is working for the common good, some factions inside the organisation work against the players and use them as scapegoats.
I don't make things complicated. That's the way they get, all by themselves.