The spirituality for fighting Muslims is the same as fighting devils.

Spiritual warfare.    

The second Vatican council took a conciliatory approach to Muslims - saying they worship the same God. But here we see that they do not see it that way. Their god Allah is differentiated from the god of the Jews and Christians. So, that Vatican declaration might be taken in the sense of James 2:19 "You believe that there is one God. Good! Even the demons believe that--and shudder." Muslims may recognize the same God in the same sense as the demons do.  And Allah is the moon god of the Bedouins - even if the word translates into G-D. There is no continuity from YHWH of Israel to the heavenly Father of Jesus vs muhammed's sock puppet allah.

So, it is consistent with an approach of no tolerance, no compromise, no acceptance of evil e.g. the deceitful ways and teachings of Islam.