The Barbary Pirates preyed on American and some European shipping in the late 1700s and early 1800s, until the U.S. and British navies intervened and “persuaded” them not to. Were the pirates, and the north African potentates who sponsored them, motivated by Islam much, if at all? Did they want to smite the infidel Christians? Or did they just go after targets of opportunity, as pirates of every era have done?
According to Peter Earle in his book “The Pirate Wars” the pirates/privateers along the Barbary coast got their start in the 16th century but didn’t attain the peak of their powers until the early 18th century. They considered themselves to be fighting a war against christendom and, initially at least, were almost wholly state sponsored. The captains carried commissions from the state to attack christian shipping and to take christian slaves. By the end of their tenure they seem to have lost this “noble” calling.
Earle quotes from a French book “Histoire de la marine algerienne” (by Belhamisi) that they would read verses from the Koran as they took ships. You might try to find “Our Navy and the Barbary Corsairs” (1905) by one Gardner Allen if your French is anything like mine. 
Anyway, I think the answer is: they wanted to smite the infidel christians. Also plunder is nice.
Also of interest are the Knights of Malta which started as the christian analogue to the Barbary corsairs. They were an order of knights who sailed around on ships attacking muslims and selling them into slavery, all in the name of continuing the holy war against Islam.
Tit for tat, I suppose.
sinjin
Certainly religion formed the backdrop to the conflict, which was part of the long struggle between Christianity and Islam in the Mediterranean. The Barbary powers preyed only on Christian-owned ships and enslaved only Christian captives, and those who converted to Islam were freed.
Nonetheless, there was nothing like the Islamist ideology that we see today. The piracy was mostly a matter of loot, with the religious difference a way of easing one’s conscience (“it doesn’t count as stealing, because they’re infidel dogs”).
This doesn’t appear to be the case. According to one contemporary report by a Portuguese prisoner in the early 17th century in Algiers, when it was near the height of it’s wealth and power:
…there were some twenty thousand captives in Algiers, a good half of whom were people ‘of pure Christian stock’, Portuguese, Flemish, Scottish, Hungarian, Danish, Irish, Slav, French, Spanish, and Italian; the other half were heretics and idolaters - Syrians, Egyptians, even Japanese and Chinese, inhabitants of New Spain, Ethiopians.
From The Mediterranean and the Mediterranean World in the Age of Philip II by Fernand Braudel ( 1949, 1966 Librairie Armand Colin ).
Earlier Braudel points out:
Privateering often had little to do with either country or faith, but was merely a means of making a living. If the corsairs came whom empty handed their would be famine in Algiers. Privateers in these circumstances took no heed of persons, nationalities or creeds, but became mere sea-robbers.
This I’d agree with, with the caveat above that Muslim corsairs seem to have preyed upon their own as well.
Similarily Christian corsairs raided both Muslims and Christians, often indiscriminantly. For example in a record of 90 Venetian vessels plundered by corsairs between 1592 and 1609 for which a definite source of the attacks can be placed, Braudel notes that 44 were lost to Muslims, 24 to Dutch and English privateers and 22 to Spaniards.
So to answer the OP - I’d say the priorities were economics a dominating first, religion an oft-invoked but weak second, state or national identification a distant third.
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Tamerlane
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Tamerlane