The Hospitallers (or Knights of Rhodes, or Knights of Malta, or Order of Malta, etc., they have an inconveniently large number of names) certainly presented themselves as honourable knights defending Christendom. This is the opening to a script from the late fifteenth century, written by the English Hospitallers to solicit donations (I have modernised the spelling):
Sovereign all holy church is being to maintain all religious men and to open there hearts of pity unto them. Especially unto the noble order and religion of St John Jerusalem Knights of Rhodes who not only spare labours nor spending of there temporall goods but also be ready to spend their blood and life against Turk, Saracens, and other infidels for the defence and augmentation of Christian faith and of the city, castles, and isles of Rhodes and of great number of Christian people there inhabit under the protection... [illegible text]... of the said noble religion of St John. Which city of Rhodes a key to all Christendom standing in great peril between the cruel and mighty tyrants the Turk and sultan, enemies to all Christendom... [illegible text]... there is a great cause to move all Christian people to help the said noble religion and knights of Rhodes...
However, the Hospitallers' conduct on Rhodes and Malta often did amount to little more than piracy. From their time on Rhodes, the Order operated a system of licenced piracy called the corso. This allowed individual Hospitallers to arm their own ships to attack Muslim shipping. The Order was entitled to a portion of any booty acquired. This was later expanded to include people who were not themselves members of the Order and instead simply paid to fly under the Hospitaller flag. These men were dubbed by the Venetians as 'corsairs parading crosses'. Officially, the corso was only supposed to target Muslims and Jews. Other Christians were supposed to be exempt, but the Order often attacked Christian shipping which traded with Muslims, such as Venice's, or Christians serving the Ottomans, like the Orthodox Greeks.
Another aspect of the Order's history which clashes with some popular perceptions of them as 'honourable knights' was their participation in the slave trade. It is estimated that there were about 3000 slaves on Malta in 1590, around 2000 in 1632, and about 2000 again in the 1660s, of which 1700 were owned by the Order. The Hospitallers frequently enslaved the crews of captured Ottoman shipping, sometimes enslaving hundreds at a time. In 1563, the Hospitallers enslaved 400 people from three captured ships, 250 of which were Turks. In 1634, the Order captured an Ottoman convoy transporting African slaves to Constantinople. The Hospitallers enslaved the Turkish crew and sent any white slaves to work in their galleys, and sold the African slaves into private ownership. Of these, fourteen men and six women were sold to individual Hospitallers, five men and three women to the Order's vice-admiral, and Hospitaller chaplains bought one man and four women. Not only did the Order enslave Turks and Africans, but they also frequently captured Jews, who were often on Ottoman merchant ships. There are estimated to have been around seventy Jewish slaves on Malta in 1549. The enslavement of Jews became so common that Venice's hevrah, a society for aiding the ransoming of Jews, appointed a permanent representative on Malta in the 1640s. By 1661, the enslaved Jewish community of Malta had its own synagogue. Fear and hatred of the Hospitallers often featured in Jewish literature of the early modern period. The sixteenth-century Italian-Jewish philosopher Joseph Ha Cohen recorded an incident in 1552 in his Vale of Tears when a Jewish ship was captured by the Order:
In the year 5312 (1552), the vessels of the monks of Rhodes, who are in Malta, cruising to find booty, encountered a boat from Salonica [Thessaloniki] whereon were about seventy Jews. They captured it, and returned to their island. The unhappy victims had to send to all quarters to collect money for the ransom of their souls exacted by the miserable monks. Only after payment were they suffered to continue their voyage.
So yes, the Hospitallers did fight to defend Christendom from the Ottomans. That was their prime purpose on Rhodes and Malta. However, this didn't prevent them from also acting as pirates, something which helped fund their wars with the Turks, campaigns that were also supported by the enslavement of the many captives they took from the ships of the Ottomans or those who traded with them. The slave community was sometimes a source of love potions and other magic for the Hospitallers. The popular image of the Hospitallers as honourable, devout, chaste knights is not an entirely accurate one.
Sources:
Emanuel Buttigieg, Nobility, Faith and Masculinity: The Hospitaller Knights of Malta, c.1580-c.1700 (London, 2011).
Carmel Cassar, 'The Jews, Catholic Policy, and the Knights of St John in Malta', Journal of Mediterranean Studies, 23:2 (2014), pp. 169-84.
Molly Greene, 'Beyond the Northern Invasion: The Mediterranean in the Seventeenth Century', Past & Present, 174 (Feb., 2002), pp. 42-71.
Rory MacLellan, 'Hospitaller confraternity scripts, crusading and the English Reformation', Historical Research (Forthcoming, May 2019, early view available here).
Helen Nicholson, The Knights Hospitaller (Woodbridge, 2000).
Godfrey Wettinger, 'Black African Slaves in Malta', in Simon Mercieca (ed.), Mediterranean Seascapes (Malta, 2007), pp. 65-81.