And would the members of a majority-Muslim country particularly care if someone committed blasphemy regarding her own religion? Would "Christ" even register as a swear word?

I can't say anything about Turkey in particular, but Jesus/Isa is a major prophet in Islam, and I wouldn't be surprised if there are Muslims who object to people using the prophets' names (or titles, in this case) as expletives.

But given Pike's perception of the Muslim world, it's entirely possibly he thinks saying "Christ" could get you marked as an "infidel" or something.