I know the answer but I'm not sure you will like it.
The refugees are drawn from the refugee camps and most of the refugees are Sunni and Yzidi because most of the fighting is occurring in their territory.
Christians never made up more than 10% of the Syrian population and most of them live in Damascus and Aleppo which have been spared most of the fighting.
Life continues to be good in Damascus with oppulent parties and a still thriving tourist trade.
Most Christians in Syria still live in their intact homes.
There were some Christian refugees from Iraq early on but many of them made their way to Jordan or Israel.
The link is a blog opinion piece that doesn't lie, it just provides enough selected information to allow the reader to jump to the conclusion intended for them.
Does that mean that these are untrue?
Helping Syrian Christians
Help Syrian Christians Reach Safety
The Nazarene Fund FAQ's
I don't think that makes it sound like they are living comfortably in their intact homes. If that were so, why would they be trying to leave Syria? I can almost promise that the news media isn't telling the whole story.