I haven't ever thought of Christian privilege. I'm not aware of it, but haven't been looking for it. I think there can be a cross over where traditional British culture and religion overlap, which people would want to defend for cultural reasons rather than religious ones- sort of, William Shakespeare, King James Bible, Easter holiday, type situation.
I can get a bit aggrieved when people want in on something special which is funded/set up/maintained by religious people, but want to be able to ridicule the religion, too. So, getting married/christened in church and then creating about associated requirements, or wanting to send their children to a faith school but complaining about the faith content of the faith school. But there are grey areas as with everything. Is that christian privilege?