I was also going to agree with a part of what 'Bodhi' said, specifically:
I still find that practice Buddhism such as contemplating on what cause my suffering, such as my arrogance and desire, I can still lead a happy life that I think is worth living. I still find meditation helpful with my anxiety and decision making which lead to positive consequences.
There are passages in the Nikayas under the general heading of 'in this very life', which say something very similar and often make the point that 'the benefits of meditation' are something that can be realized without any commitment to 'a life beyond'. And I think that is quite true and perfectly laudable. if that is what a 'secular approach' to buddhism means, then I would have no issue with it whatever.
However there is also an undercurrent in the debate, which I think you're picking up on, which is part of the big debate between 'religion' and 'science' in the modern world.
I myself am quite a 'secular Buddhist' - I live and work in a typically modern western lifestyle and culture. But I have realized that commitment to Buddhist meditation is in some way 'religious' insofar as it requires you to accept certain principles which really have no counterpart in secular philosophies. It is what Indian philosophy would call a sadhana
or a spiritual discipline, even if one is far from a perfect exempar or practitioner of it. And that brings with it certain ways-of-understanding, which, I think, are not really part of western secular-scientific thinking or part of our modern cultural milieu.
Where I part company with the secularists such as Harris (and Bachelor and many of the other 'secular buddhist intellectuals') is that they have a strong commitment to 'scientific method' in areas where i really don't think it has any applicabillity. This leads them to particular ways of thinking about the meaning of such ideas as karma and rebirth which I don't think are even really justified by science, as such. After all, as we have discussed, the scientist Ian Stevenson gathered quite a lot of empirical evidence concerning children who recall previous lives. I find that many of the so-called 'secular buddhists' are not really prepared to even consider such evidence, because they have already decided that belief in rebirth is a 'cultural accretion' or 'not really part of buddhism'. And that, I think, is not so much a 'scientific' attitude, as 'the scientific worldview' speaking, and they're different things. It's not even a really scientific attitude.
In the beginner's mind there are many possibilities; in the expert's mind there are few ~ Suzuki-roshi