Nah, there are Turks and they won't be seen as Crusaders of any sort.
They are merely the "Old Ottoman Caliphate" reasserting their claim and guardianship of Islamic Holy Sites, just like what they've already done within Israel borders.
While the ships could be crewed with Italians, the later won't step out of coastal areas as the land invasion of the Holy Cities mustbe conducted pretty much exclusively by Turkish, Libyan, and Berber Muslims if they wanted to not poking on religious issue too much.
Would Turkey's government ITTL speak of the reconquest of Mecca in religious terms, or would it be more from the perspective of nationalist pride?
Hell, I imagine a certain young Libyan Colonel may ended up being trusted Italian representative at Mecca, while certain young Turkish Cleric ended up being Keeper of the Masjid-il-Haraam.
Now that would be an interesting AH possibility: Qaddafi growing up an Italian subject.
What would Qaddafi be liked if he lived under the velvety iron glove of Italian fascism? Would he assimilate into Italian society for personal gain? Would he be a more moderate nationalist? Or would he still be the same quasi-feudal warlord masquerading as a revolutionary?