Chirstianity = beliveing that Jesus is the messiah (christ)
The Koran doesn't teach that Jesus is the messiah and claims that he never died on a cross which makes being a true Muslim and a true Christian impossible.
Not only that but the Koran forbids friendship with Christians and Jews...
O you who believe! do not take the Jews and Christians for friends; they are friends of each other and whoever amongst you takes them for a friend then surely he is one of them; surely Allah does not guide the unjust people.