Only an idiot (or a muslim) would think it's a good idea to hand over Christian land and property to an islamic Kurdish state.
And what Christian land and property would be handed over to Kurdistan? Your point is not valid. You live in the US. If you own a house there, is it the property of the state or federal government? Is Kurdistan presently in a Christian state?
There are both Christians and Jews living in Kurdistan. Both of their lingua franca is Aramaic, and the Kurds are not, as far as I know, interested in persecuting them.
The important point that you are missing, is that if Iraq, Iran, Syria and Turkey are partitioned to make a Greater Kurdistan, it would take important assets such as oil, arable land and fresh water away from Erdogan, Iran, Assad, Iraq and ISIS. If they predictably refuse to be partitioned, that can be used to resist the pressure on Israel to partition for the sake of the Palis.
It is win-win, and Christians would be at worst still living in the ME and not anymore harmed as Kurdish citizens than they would have been remaining Turkish, Iranian, Iraqi, Syrian or ISIS dhimmis, perhaps even helped, if Israel, the Vatican, and President Trump have anything to say about it. The UN and EU can of course be counted on to not be counted on.