Right. And as liberal as Islam is wrt 'People of the Book', they are very, VERY clear that Islam is final. No prophets after Mohammed, no new religions after Islam, if you convert to Islam, that's it, no going back. And, of course, no way can any (true) Muslim convert.Because actual members of the imperial family would have to become apostates. Not good PR for the dynasty.
So, while it might, in theory, be possible for a Sultan to marry off a daughter to a firengi, I think it would create as (least as) many problems for him as for those European monarchs that POd the Pope enough that their whole country was put under the Inderdict. Now, there were monarchs that did that, but no many and they usually had to grovel at the feet of the Pope thereafter (almost literally).
I could imagine a Sultan TRYING it, for what SEEMED like good enough political reasons, but I'd bet he'd regret it, oh, so badly.