Ok, this came out yesterday during a game:

I have Syrio Forel in the shadow area and my opponent has another shadow card face down.

My opponent is the first player and at the beginning of the challenge phase he decided not to turn face up that card from shadow. So it's my opportunity to bring syrio out of the shadows and I take it.

At this point my opponent turned Varys face up, discarding my syrio (before syrio there weren't ally in play, that's why he didn't bring Varys out).

Can he do that? My opponent tried to convince me by quoting this rule:

After a player’s action resolves, that palyer must
allow each opponent (in clockwise order) the opportunity
to take an action or pass. A player may
not take another action until all opponents have
taken an action or passed.

But I checked on the rules of the shadow mechanic and I found this:

When more than one player want to bring a card out of Shadows at the
beginning of a phase, the players do so one at a time, starting with the
first player and proceeding clockwise. This happens before any other
“beginning of the phase” effects occur. Each player has one chance to
bring a card out of Shadows each phase. If this opportunity is passed,
it is lost until the beginning of the next phase.

Who is right?

The Fists Player can bring his card out of shadows first. If he doesn't, he loses the opportunity ti bring cards of shadows for that phase and the next player can bring his card out of shadows.

thorin_81 said:

Bringing cards out of Shadows is not a standard player action so the rules for Player Action Windows (quoted by your friend/opponent) do not apply. Bringing cards out of Shadows is more like initiating challenges in the Challenge Phase. If you are the first player, you have an opportunity to initiate your three challenges. If you pass on any of those opportunities, you do not get to go back and initiate them later after your opponent has done his.

The order described in the Shadow rules - wherein if the First Player passes, he is Out of Luck for the phase no matter WHAT the next player brings out od Shadows - is the proper way to go.