I think it depends on how you define 'greatly influenced'.

I seem to recall a bit in the Bible about not stealing, so it's fair to say that pirates weren't great Christians. But, they were Christians on the whole. They were people of their time: their social systems and political outlook were the same as other sections of society and, like almost everyone else in the Anglophone world, they had been brought up as Christians and, on the whole, remained so. That said, if you take any large enough group of people you will naturally find different levels of commitment to their faith.

On one occasion a pirate company tried (unsuccessfully) to conscript one of their captives to act as a ship's chaplain. Perhaps the most interesting allusion to the pirates' adherence to their Christianity was in the supplies sent by New York merchant Frederick Phillipse to his agent at St. Marie's Isle, Madagascar, Adam Baldridge. Baldridge arrived at St. Marie's in 1689 to establish a trading post there in order to trade with the pirate companies then infesting the Indian Ocean. Phillipse sent 'Western' commodities, otherwise unavailable in the region, which Baldridge sold to the pirates operating there in exchange for their pillaged loot, which was sent back to New York for Phillipse's profit. The good sent by Phillipse included things like clothes and tools, but also 'some books, Catechisms, primers and horne books, [and] two Bibles...' (Deposition of Adam Baldridge, 5 May, 1699, CO 5/1042, no. 30ii)

The various 'last words' pamphlets published to accompany the execution of pirates suggest that most pirates facing execution re-found God in their last days. The propaganda nature of these pamphlet means they must be treated with caution, but there are exceptions, in which some pirates facing the gallows are vilified for their refusal to surrender themselves to God, which suggest that there may be some element of truth in the others. At the trial of the survivors from Sam Bellamy's crew in Boston in 1717, Thomas Fitzgyrald, master of the Mary Anne, which had been captured by the pirates and was run aground in the same storm that finished Bellamy and the Whydah, deposed that the pirate prize crew aboard his vessel 'Cryed out saying, For God's sake let us go down to the hould and die together. And the whole Pink's company tarry'd on board her all that night: and in their distress the Prisoners [ie. the pirates on trial] ask'd the Deponent to read to them the Common-Prayer Book, which he did about an hour.' (The Trials of Eight Persons Indited for Piracy, [Boston, 1718], pp. 9-10)

There appears to have been little Catholic-Protestant rivalry, principally because the overwhelming majority of pirates in the 'golden age' came from a Protestant background. However, snippets of evidence do suggest that pirates were as aware of the differences between different branches of Protestantism as everybody else at the time. In the trial mentioned above, for example, one victim deposed that he had been abused as a 'Presbyterian dog' (p. 20). According to Jacob du Bucquoy, it was one of Richard Taylor's company's articles that 'In order to preserve the peace and union necessary between members of the brotherhood, quarrels and insults are forbidden, likewise religious disputes.' Which suggests that religious factionalism was an issue for some pirates.

Overall, though, du Bucquoy gave probably the most succinct summary of religion among the pirates:

'In all the time that I, to my great displeasure, spent with them, I never saw them engage in the visible practice of any religion whatsoever. They take oath on the Bible, but they never read it. The only custom they observe which seems to show any respect towards God was that whenever they are able they rest on Sundays. When one of them dies they chant a Psalm or canticle while escorting the body, but that is rather a custom left over from their earliest education than a sign of their submission to God.'

Translated from Jacob du Bucquoy, The Sixteen Year Voyage in the Indies made by Jacob du Bucquoy, full of remarkable adventures, notably those which he experienced during his mission to the Delagoa River (Harlem, 1745). Extracted in E.T. Fox, Pirates in Their Own Words (Okehampton, 2014)

Was there a Catholic-Protestant rivalry at sea?