It's worth pointing out that your question seems to at least implicitly suggest that an alliance with a non-Christian power was out of the ordinary. This isn't really the case -- the Crimean war a few decades before had seen the United Kingdom and France support the Ottomans in a war against Russia, and other examples (including the Franco-Ottoman alliance against the Habsburgs in the 16th century, or France taking part in the later Thirty Years war on the ostensibly "Protestant" side) of politics trumping religion in military alliances abound. Religion can certainly play a major part in setting up the players in a conflict, but a European-Ottoman alliance wasn't entirely novel. Of course, it's very possible that this isn't news to you; I may be reading too much into your question.