What proportion of Christians worldwide identify as Christian for social/cultural reasons rather than religious conviction?
It would be difficult to come up with a specific percentage.
Those who call themselves Christian for financial or social advantage usually do so when Christianity is an ascendency. Like when Christianity was made official in the Roman empire in the fourth century and in America during the 19th and 20th centuries. In Europe during the middle ages you may have seen some pretend Christians not necessarily for advantage but survival because there would be penalties for trying to live as a non-Christian.
There have always been Christians (or any other religion) that are of that religion for what might be called familial inertial reasons. Legacy or heritage members of a religion would be hard to distinguish until that religion became persecuted and they took advantage of the opportunity to leave the religion.
The reaction of Christians to a world hostile to them was described by Jesus;
Luke 9:26 For whosoever shall be ashamed of me and of my words, of
him shall the Son of man be ashamed, when he shall come in his own
glory, and in his Father's, and of the holy angels.
Whatever the percentage is today it would be shrinking because it is starting to become a disadvantage to be a Christian.