I don't know where this "because of who we are" claim has ever been backed up. Bin Laden issued his 'fatwa' or declaration of war, or whatever it was and spelled out his grievances.
He was enraged over our basing our infidel selves on sacred Saudi Arabian soil. He was angry that we support insufficiently pious Arab leaders, which is just about all of them in his view. There was no mention of our mere existence setting him off. It was our presence, our power projection in the Arab world.
As for Iraq, Bin Laden had approached the Saudis before Gulf War I and offered his services to drive Saddam out of Kuwait. He didn't have any love for Saddam, who was hardly a moslem cut from the Bin Laden mold.
I say he hates us for who we are because radical Islam is, by definition, at war with all non-Muslims, especially Christians. Allah is a god that makes comprehensive claims as being god of the entire universe. His followers are prepared to press those claims with a global jihad.
The long-term goal, by definition then, is the unification of the Muslim world in a civilizational conflict with the West, with the hope of establishing a global Islamist empire. They are far from this goal, and it seems fanciful, but we need to guard against it. That is why I say that the terrorists hate us for what we do and who we are.
But that certainly didn't stop them from working together, which they did despite the media's claims, or stop Zarqawi from setting up shop in Iraq. It wouldn't have stopped them in the future either. Saddam would have done what was in his interest, and his interest was in staying in power and sticking it to us whenever possible.