In the article entitled A Secular Evaluation of Rebirth, Doug Smith, of the Secular Buddhist Association, wrote:
It is for reasons such as these that any contemporary, scientifically informed Buddhist practice should reject belief in rebirth and its associated kammic causation. The Path is rich enough without them.
It appears that many Secular Buddhists do not accept rebirth, while almost all other Buddhists do.
In the essay entitled Dhamma Without Rebirth?, well-known Tripitaka translator and scholar Ven. Bodhi conveyed the mainstream view of the Buddhist world:
If we suspend our own predilections for the moment and instead go directly to our sources, we come upon the indisputable fact that the Buddha himself taught rebirth and taught it as a basic tenet of his teaching. Viewed in their totality, the Buddha's discourses show us that far from being a mere concession to the outlook prevalent in his time or an Asiatic cultural contrivance, the doctrine of rebirth has tremendous implications for the entire course of Dhamma practice, affecting both the aim with which the practice is taken up and the motivation with which it is followed through to completion.
If someone considers himself a Buddhist, we can assume that he accepts the Four Noble Truths and the Noble Eightfold Path. I guess this should apply to Secular Buddhists as well.
If there is no such thing as rebirth (or continuation of the stream of consciousness or mind after death, in a new life), then there is no need to end suffering by ending craving (third noble truth), through following the Noble Eightfold Path (fourth noble truth). Instead, it's much easier to commit suicide, or simply wait for natural death. After all, if there is no rebirth, then at death, all suffering would end anyway, right?
So, based on this, how do Secular Buddhists justify their acceptance of the Four Noble Truths and the Buddha's teachings in general, if they reject rebirth? How would the Four Noble Truths and Nibbana have any meaning or usefulness for them? Why would they choose to follow the Noble Eightfold Path, if death is a much simpler way to end suffering?