Plus, the context of the times are completely different.
In late 2002-early 2003, the US is still enjoying its unilateral moment. Its relative decline in power had not begun. Russia and China weren't as assertive. Russia was barely two years removed from the chaotic Boris Yeltsin years. China, though rising, wasn't the self-evident and confident power that it is today.
Add in that not even two years had passed since the 9/11 attacks, and no state was going to put real, serious effort at getting in America's way. In that sense, it is telling that the biggest obstacle to the attack on Iraq was France, a country that, in the big picture, is a US ally.
Contrast with today. Russia turned itself around and has reasserted itself through its oil power. China is the clear number 2 power on the planet, and confident of such. And the U.S. has spent a decade mired in inconclusive warfare, a superpower bogged down in "colonial" counterinsurgency affairs, a devastating economic crisis, etc.
It isn't that China/Russia "didn't give a shit" about Iraq back then, but somehow do about Syria and/or Iran today. It's that enough has changed over a decade in the relative balance of power that they feel confident enough to assert themselves on the subjects that they "give a shit" about.