What is the Catholic Church's Official Stance on ISIS?
If you go by the utterances of the current Pope, there does not appear to be a coherent policy and the "official stance" appears to vary if the Pope is seen to be a credible spokesman for the Catholic Church. (See examples below). I have not seen an encyclical nor a Papal Bull of late enunciating a policy. If one comes out, this answer will need to be updated.
Has Pope Francis actively encouraged the world's most powerful militaries to remove ISIS from the battlefield?
No. He's not much of a militant pope, unlike Pope Urban II
Here is what the Pope has offered up to the media.
The Pope Condemns ISIS. (2014)
Thousands of people, including many Christians, driven from their
homes in a brutal manner; children dying of thirst and hunger in their
flight; women kidnapped; people massacred; violence of every
kind”—Pope Francis was clear in his condemnation of the actions of the
militants of the Islamic State in Iraq and Syria in his remarks on
Aug. 10: “All this greatly offends God and humanity. Hatred is not to
be carried in the name of God. War is not to be waged in the name of
God.” In a letter to U.N. General Secretary Ban Ki-moon on Aug. 9,
Pope Francis appealed to the international community “to take action
to end the humanitarian tragedy now underway.” He added, “The violent
attacks that are sweeping across Northern Iraq cannot but awaken the
consciences of all men and women of goodwill to concrete acts of
solidarity by protecting those affected or threatened by violence and
assuring the necessary and urgent assistance for the many displaced
people as well as their safe return to their cities and their homes.”
The Pope is an apologist for ISIS
“Today, I don’t think that there is a fear of Islam as such but of
ISIS and its war of conquest, which is partly drawn from Islam. It is
true that the idea of conquest is inherent in the soul of Islam.
However, it is also possible to interpret the objective in Matthew’s
Gospel, where Jesus sends his disciples to all nations, in terms of
the same idea of conquest.
“In the face of Islamic terrorism, it would therefore be better to
question ourselves about the way an overly Western model of democracy
has been exported to countries such as Iraq, where a strong government
previously existed. Or in Libya, where a tribal structure exists. We
cannot advance without taking these cultures into account.”
The Pope is mildly deluded.(2016)
He said: "We have a mission to convert all non-Christian religions’
people [except] Judaism." He added: "It is very clear that we can
speak about three Abrahamic religions but we cannot deny that the view
of Abraham in Jewish and the Christian tradition and the Islamic
tradition is not the same.
In a similar utterance, he opines that "this is not a religious war" to which ISIS responded "yes, it is a religious war."
He refuses to confront the truth of ISIS. (2016)
The Pontiff condemned 'every form of hatred' and offered his prayers
to those involved. Vatican spokesman Jesuit Father Federico Lombardi
issued a statement on the Pope's behalf after two ISIS knifemen
stormed a church in Normandy this morning. He added that the Pope was
particularly appalled by the 'barbaric killing' because it happened in
a sacred place. He went on to describe the attack as another act of
This last one is the most difficult to assess given his position. ISIS "soldiers" attack one of his priests, but ISIS' hatred of Christians isn't the topic of the Pope's remarks, but the vague "every form of hatred" gets condemnation. A change from 2014, when he appealed to the UN for help ... or something.
Policy derived by analysis: the Pope (and by association, the Catholic Church) hopes that someone will deal with ISIS as he wrings his hands and the Church prays for the conversion of ISIS and its followers. That last bit is at least consistent with Lumen Gentium, which was an official utterance of the church after Vatican II.
That is the only "policy" I can arrive at when examining the conflicting utterances offered up by the head of the Catholic Church.