What would they do, if no one believed them?
Frankly? The only one that matters to believe I am a Christian is Christ. Issuing a press release claiming I am a sheep and not a goat would gain me nothing. Getting my neighbor to agree that I am a Christian gains neither him nor me anything.
However, lets see what Jesus says about the issue
Matthew 25:
When the Son of Man comes in His glory, and all the angels with Him, then He will sit on the throne of His glory. All the nations will be gathered before Him, and He will separate people one from another as a shepherd separates the sheep from the goats, and He will put the sheep at his right hand and the goats at the left. Then the king will say to those at His right hand, “Come, you that are blessed by my Father, inherit the kingdom prepared for you from the foundation of the world; for I was hungry and you gave me food, I was thirsty and you gave me something to drink, I was a stranger and you welcomed me, I was naked and you gave me clothing, I was sick and you took care of me, I was in prison and you visited me.” ... “Truly I tell you, just as you did it to one of the least of these who are members of my family, you did it to me.”
Then He will say to those at His left hand, “You that are accursed, depart from me into the eternal fire prepared for the devil and his angels; for I was hungry and you gave me no food, I was thirsty and you gave me nothing to drink, I was a stranger and you did not welcome me, naked and you did not give me clothing, sick and in prison and you did not visit me.” ... “Truly I tell you, just as you did not do it to one of the least of these, you did not do it to me.” And these will go away into eternal punishment, but the righteous into eternal life. (Matthew 25:31-36, 40-43, 45-46 NRSV)