This is an excellent example of why the more fantastical the claim, the larger the burden of proof. If you tell me your name is John, I am happy to accept your name is John until I am provided evidence otherwise. If you tell me you are the re-incarnation of John the Baptist, I am likely to disbelieve you outright. Can you see the difference there?
A paternity test would have little bearing on the relationship between your friend and his father. His father is likely to continue to treat him the same regardless of the results. The father's claim that he is the paternal father is not a very fantastical claim.
The claim that there is a benign, omnipotent, omniscient being is a fantastical claim.
Consider a friend tells you that he believes in fairies. He can not provide any evidence whatsoever because they only appear to him. You are likely to disbelieve him, but you are happy to allow him his delusion. A day later, your same friend approaches you and says the fairies told him that he needs to kill someone to appease them. Would you demand proof now? Would you require more proof now than you would when he just said he believed in fairies?
Most mainstream Christians may not be claiming god is telling them to kill people, but there are plenty that want to demonize certain 'sinners'. As rational people, is it not our responsibility to demand some kind of proof to validate their claims?