What reading I've done on it has been of the Barbary coast pirates, with some notes on the Knights of Malta carrying on their own slave raiding.
Did other Christian powers engage in slave raiding on North Africa? To what extent? Where did they sally from and where would they attack? Were these acts encouraged by the monarchs of these territories? What about the Church?
The Knights of St. John of Jerusalem, better known as the Hospitallers, were a Christian military order that definitely engaged in raiding and piracy. From 1309 to 1522 A.D., they were based on the island of Rhodes in the Aegean Sea, and they attacked and seized Islamic trade ships in the eastern Mediterranean. Muslims taken captive were sold as slaves. The Ottoman Turks attempted to crush the knights in 1480, but failed to capture the island. Their second attempt, in 1522 under Sultan Suleiman the Magnificent, was successful; the knights surrendered and were given safe conduct. The Hospitallers soon relocated to Malta, where they kept on raiding Islamic ships and enslaving Muslims.
As for other Christian states, Spain was the main participant. The Spanish attacked and seized several cities on the North African coast in the early 1500s. Eventually they lost almost all of them to Hayreddin Barbarossa, an Ottoman admiral, but they held them for a few years.
In 1535 Charles V, the Hapsburg emperor and ruler of Spain and Austria, assembled over 30,000 soldiers and hundreds of ships, and attacked Barbarossa's naval base at Tunis. He destroyed Barbarossa's fleet, forcing him to flee, and thoroughly sacked and burned the city, killing many of the city's inhabitants and enslaving others. Charles even had a tapestry commissioned to commemorate his triumph: http://www.flandesenhispania.org/tapestries/index.php/The_Conquest_of_Tunis_series
So yes. Some other Christian powers did engage in piracy, slave raiding, and attacks on north Africa and in the Mediterranean, although not as much as the Barbary pirates. Spain, the Hospitallers, and some of the Italian city-states such as Venice and Genoa were the major participants. After the 1500s, they mostly focused on raiding Muslim shipping and protecting their own vessels, so slave raiding on North Africa puttered out. The Catholic Church's attitude varied: sometimes the popes were allied with other powers against Spain and so offered no encouragement, and other times they took the lead in brokering alliances to combat the Barbary pirates and Turks.
Sources: Will and Ariel Durant, "The Reformation: The Story of Civilization, #6."
Lord Kinross, "The Ottoman Centuries: The Rise and Fall of the Turkish Empire."