It wasn’t as controversial as you might expect, since by the time the Ottomans claimed the caliphate in 1517, they controlled most of the Arab world already, and there hadn’t been a caliph who’d ruled in his own name for … well, a very long time. At least 5 centuries—it’s hard to say for certain as the Abbasid caliphs were almost always dealing with a power behind the throne, as well as rival claimants (at one point there were 3: the Umayyads of Spain and the Fatimids of Egypt also claimed to be caliphs). After the fall of Baghdad to the Mongols in 1258, the Abbasid line relocated to Cairo where they were basically kept around as well-kept political prisoners by the Mamluks — I couldn’t, off the top of my head, name a single caliph during that period. The conditions under which the actual title was handed over to Selim III are a bit opaque—there’s an official version, but all is a bit unclear in the historical record.

So, one could say that the title was rather tarnished and had lost a lot of its symbolic meaning within the Arab world — the caliph certainly wasn’t a prestigious person, but rather conferred prestige upon the Sultan of Egypt when he was trotted out occasionally at state ceremonies and coronations and things like that.

What the Ottoman conquest did do, interestingly, was excite other non-Arab Muslims about the possibility that they could legitimately aspire to the caliphate—rivalries with the Safavid Persians, for example, were exacerbated as the stakes were raised. It also gave the Ottomans their long-desired legitimacy in their own right as rulers over much of the Arab and Islamic world.