As Allen points out, the support is there and it is surprising given past history:
Archbishop Giorgio Lingua, the pope’s ambassador to Baghdad, told Vatican radio that the American strikes are “something that had to be done, otherwise [the Islamic State forces] could not be stopped.”This is in contrast to strong Vatican opposition to the US-led war in Iraq in 2003 and the UN and US-led war in 1991. Even in 2001, with the US attacks against the Taliban in Afghanistan, Vatican reaction was mixed to negative. Allen attributes this to a kind of stark realism on the part of the Vatican which has not passed its time:
Lingua spoke plaintively of the ordeals faced by an estimated 100,000 Christian refugees from northern Iraq – many of whom, he said, are children – to account for his view of the American campaign.
“You can see these kids sleeping on the streets,” Lingua said, adding, “[there is so much] suffering.”
In a similar vein, Archbishop Silvano Tomasi, the Vatican’s envoy to the United Nations in Geneva, told Vatican Radio that “military action in this moment is probably necessary.”
One core reason the Vatican opposed the two Gulf Wars, as well as any expansion of the conflict in Syria, was fear that the fall of a police state in the Middle East would lead to the rise of a radical Islamic theocracy in which Christians and other minorities would find themselves in the firing line.This certainly seems like a plausible ex post rationale, but is there any evidence that in 1991, 2003, and 2013 Vatican thinking was indeed driven by the idea that it was better to keep Middle Eastern police states in place in order to prevent radical Islamist regimes from coming to power? I remember vague discussion about violence never solving anything, but I don't recall anything specifically making this argument and in some ways it seems out of character.
That’s no longer a theoretical anxiety. It’s the lived reality of the new caliphate proclaimed by the Islamic State, which means that the Vatican and other Christian leaders are no longer so worried about the aftermath of a conflict. They’re much more preoccupied by the here and now, and thus more inclined to back anyone who seems prepared to do something about it.
This is not actually the first time that the Vatican has come out in support of US-led military intervention in the last few decades. While John Paul II was strong in his criticism of every other US military intervention during his pontificate he was actually quite supportive of the US intervention in the former Yugoslavia to prevent ethnic cleansing and mass killings. Indeed, the Vatican was in some ways ahead of the US supporting humanitarian intervention with military means, something which some Balkan actors continued to resent till John Paul II's death.
One common thread here is clearly a willingness to support the use of force to halt an immediate humanitarian catastrophe, but not to remove a rogue state government. However that doesn't appear to be a constant principle. I don't recall the Vatican being open to military force being used in Rwanda or to halt mass killings during the Syrian civil war. However, think the common thread which could be identified is one of rarely supporting military force in a "humanitarian intervention" context, subject to certain other criteria -- not some sort of realpolitik in which it's better to keep repressive governments in the Middle East in place in order to preserve order and prevent an Islamic State.