Article 1, Section 10 forbids states from making treaties, and under certain circumstances from enacting trade sanctions or entering into treaties or wars.

What's the part that "specifically disallows the states from conducting foreign policy" apart from those? What's the part that forbids-- or even discourages-- a state from registering a formal advisory opinion on a question of federal law and foreign policy, i.e., the war?

There's limited useful conducting of foreign policy that a state can do if it cannot "enter into any Agreement or Compact" with a foreign power, or indicate its disapproval of a foreign government through the force of trade sanctions, or even require that a foreign company make a disclosure that would open it to liability under a state's law that is contrary to federal policy. Certainly a state can have speech that might run counter to the federal government's, e.g. if the federal government's policy was to be attentive rhetorically to the EU's concern about the death penalty, Texas still can thumb its nose. Similarly, a state can register a formal advisory opinion on a question of foreign policy.

But unlike what it can do with environmental policy, which is to some degree set its own that has real, practical effect (California is a particularly good example, with its higher-than-federal standards on emissions), it cannot set that foreign policy in any useful way. The vetoed measure noted the number of Californians who'd been killed in the war, but the governor could not declare that the state of California was at peace with Iraq's insurgents and therefore no California Guardsmen were to fight in Iraq. I have no constitutional problem with the measure (though I find any sort of "(Not) In My Name" silly); my constitutional problem is with drawing a comparison between states' ability to set environmental policy for themselves versus their ability to set foreign policy for themselves.

Moreover, I think the day has passed for state governments to announce their opinion of the federal government's relations with a foreign power. Perhaps this was appropriate when the state legislature was electing the Senators who would play a major role in the formation of foreign policy, but not post-17th Amendment. And having the people of a state discretely voice their opinion of foreign policy through a referendum isn't much more sensible. President Bush wasn't elected by the approval of Californians, and their disapproval, particularly qua Californians, is unlikely to shake his convictions.