Or any time during the modern period, really, I just thought WWI would be the best expamle. Did any of the Christian allies have goals for retaking Jerusalem (from the Ottomans, in the case of WWI) and surrounding areas for holy purposes?
Sort of? At the strategic level, allied war aims were generally quite practical, and I think you could argue much better conceived than any of the strategic aims on the western front. These included what I would describe as three primary goals: 1. Initially, to protect the Suez Canal from Ottoman incursions as a defensive measure, then, upon taking the offensive, thecreation of a buffer territory on the far side of Sinai to protect the Suez Canal. 2. Securing Mesopotamia, in general to protect the Persian gulf and at least initially to guarantee oil supplies from Persia through Basra. 3. Securing the Bosporus Straits.
These three aims corresponded to three major military campaigns: the Gallipoli landings, the British expeditionary force in Mesopotamia sent from India, and the defense of the Suez Canal which then transitioned into the Palestine campaign.
From this strategic perspective, at least on the British side and as outlined by the war aims described by the DeBunsen commission, “holy purposes” didn’t really enter into the equation.
At the political and personal level, however, it was a different question entirely. For instance, in the political wrangling over what would eventually become Sykes-Picot, French claims to Syria were in part based on their Crusades-era occupation of the area. Their claim to what would become Lebanon, in particular, was based on their Catholic affinity with the then-majority Maronites.
Palestine, and Jerusalem in particular, were so politically contentious between Britain (Protestant), but especially France (Catholic) and Russian (Orthodox), which denominations have the largest and oldest presence in the city, that in negotiating the Sykes-Picot agreement (which now included the Russian minister Sazonov) that they simply shaded the territory in brown and said it would be an international zone.
The religious motivation for the Balfour Declaration is also worth noting. While the most prominent Zionists of the day were basically secular Jewish nationalists like Chaim Weizmann, their gentile interlocutors in the British government often had other ideas. Both Balfour and David Lloyd-George were men with a strong Christian background and upbringing, and although the British government had other aims in mind as well (some practical, some, ironically, actually anti-Semitic) they nonetheless found the notion of restoring the Jews to the Holy Land to be a deeply appealing one.
Lastly, the symbolism of the capture of Jerusalem and Palestine itself was not lost on the commanders on the ground. Though they wanted to avoid fomenting sectarianism or holy war among Ottoman Muslims, Crusader imagery and terminology was unavoidable. General Allenby, on taking the city, is reported to have said “Only now have the Crusades ended.”
Although the United States did not declare war on the Ottoman Empire when it entered the war, Wilson’s 14 points forced the allies to reevaluate many of these aims and goals. National self-determination became the watchword, despite the publication of Sykes-Picot by the Bolsheviks in 1917, which the Ottomans tried to use to foment popular anger. In any event, the end result was a final settlement that at least in theory was based much more on the modern conceptions of rights, international order, and self-determination (even if in practice it was just the same old imperialism) than it was anything based on crusades and holy land.