What is the ruling on celebrating a person's birthday on their annual birth anniversary, and does the ruling change if the celebration is delayed by one day with the intention of differing from the Christians?

A person celebrating his birthday or the birthday of another is not permissible, because it involves imitating the disbelievers and emulating them. The righteous predecessors did not celebrate it; rather, they considered the passing of days a decrease in their lifespans. Advancing or delaying the celebration does not change its ruling.