Darkgamma said:
Well, I'm not as versed in Ottoman history, really

Appears you're right again I thought the title was kept further down the line
It's cool man. Mehmed II is a particular interest of mine. Really the whole issues surrounding "Roman heritage" are quite fascinating so I'm always happy to discuss it. It certainly would've been cool if the title was kept beyond Mehmed II.
I see what you mean with the "anti-pope" thing now, I was just confused with it being compared to the Caliphate. Then an Anti-Calip would be challenging the political power of another due to reasons X, Y, and Z. However how would this impact religious authority in game, and should it?
Right, glad we're on the level now then. I think in CK2 terms it probably wouldn't mean much, unless it was used as a tool to declare independence from another power, in the way that the Andalusians used it. Then again, Abdul Rahman the third was already a king when he declared himself a Caliph, so I guess it would only work for Kings under the rule of Emperors who also have a Caliph in their side. So this is probably a bit too specific a situation, right? I think in game terms it's not really a useful concept.
Just to be a nitpick: Can Abdulrahman the third's rulership be considered an "Anti-Caliphate"? His declaration is treated or seen as an affirmation of the existence and continuation of the Ummyad Caliphate in Andalusia and that those in Baghdad were usurpers.
Well, that's a good question, and I'm sure we could both write lengthy academic papers on the subject, so let's avoid doing that lol. But yeah - Rahman's was an interesting branch of the Umayyad dynasty. Was their claim to the Caliphate legitimate? I think so. Were they the "true Caliphate"? I don't think that's for us to decide, really. Were they any more legitimate than a Shia Caliph in the east? I'm not sure, as the Fatimids had a legitimate claim as well.
I can see where you're going, though - the Umayyad Caliphate was much older and one could make an argument that it was those in the east being the usurpers. That is definitely a position you could take, and probably the position Abdul Rahman the third took when he proclaimed a Caliphate, given that, as you've stated, he claimed it was a continuation of the Umayyad Caliphate.