What do secular Buddhists say about Nirvana?

Regarding the secular aspect. Many Mahayana schools of Buddhism, including at least some Zen sects and some Tibetan Vajrayana lineages, understand the supernatural as skillful means (upaya), that is to say, as useful metaphors/simplifications pointing to the real, but non-obvious, aspects of the so-called "reality".

This is not to say that these schools subscribe to a naive form of materialism. Rather, this means that the Mahayana Buddhism (as much as I can claim to understand it) is non-dualistic in its nature. It denies existence of multiple types of principally different stuff, like consciousness made of some essence that scientists can't see with their tools, and other types of dualistic "magic". Instead, in non-dualistic Mahayana view, "the magic" and the mundane are made of the same stuff, and are inherently interlocked as two aspects of the same nature.

From this standpoint, there is no need to posit any special kind of "secular" Buddhism, because Buddhism, from such a standpoint, already is and always has been non-theistic. Now, for practical reasons, I would not mind if Sat-Dharma presented itself as Secular Buddhism in this age, as an time-appropriate kind of upaya. This could work very well, as long as we respect the crucial difference between the perspective presented in the previous paragraph vs. the crude materialistic perspective of pretending that the "subtle" side of phenomena does not exist, which would be like throwing the baby out with the water.

While there is considerable variety of views amongst people who identify themselves as secular Buddhists, they all seem to converge in rejecting what is often loosely called "metaphysics". This means that they reject all forms of belief that are not rooted in science and/or common sense. Thus they reject any and all supernatural entities, forces, or states, not so much from an ideological point of view, but because of a long history of such things being debunked; because of the exposure of many, many hoaxes; and because the theories of science are so very successful and the supernatural is ruled out by these theories.

Secular Buddhists seem to identify with the European Enlightenment which aimed to free people from the despotism of the Church, the oppression of superstition, and general ignorance. Secular Buddhists take nothing on faith, whereas traditionalist Buddhists take a great deal on faith.

Some answers to these specific questions can be found on the Secular Buddhist Association Website. http://secularbuddhism.org/. Doug Smith, who holds a PhD in philosophy, has written a number of essays on these and related subjects, for example he says:

"Nevertheless from my limited perspective on the path it would seem as though nibbāna is not, should not, and cannot be entirely beyond our ability to comprehend. If it were, it would be of correspondingly scant interest to us. Therefore we are to take expressions of its ineffability as a kind of poetic attempt to express the extremity of its greatness. Nibbāna is the extinction — or perhaps the near extinction — of greed, hatred, and certain forms of ignorance. And parinibbāna does not amount to some “diffuse, indeterminate” way of being, but rather is the simple death of an enlightened person, without remainder." - Two Issues With Nibbāna.

Elsewhere (Can a Layperson Attain Nibbāna?) Smith discusses the traditional view that only monastics can attain nibbāna and gives a response from a secular point of view.

Perhaps the most prominent secular Buddhist is Stephen Batchelor, a former monk and translator of Buddhist texts. He has downplayed the issue of nibbāna

I am a secular Buddhist. It has taken me years to fully “come out,” and I still feel a nagging tug of insecurity, a faint aura of betrayal in declaring myself in these terms. As a secular Buddhist my practice is concerned with responding as sincerely and urgently as possible to the suffering of life in this world, in this century (our saeculum) where we find ourselves now and future generations will find themselves later. Rather than attaining nirvana, I see the aim of Buddhist practice to be the moment-to-moment flourishing of human life within the ethical framework of the eightfold path here on earth. – Stephen Batchelor, “A Secular Buddhist,” Tricycle Magazine, Fall 2012.

Of course this rejection of the supernatural, and nibbāna in particular, has wide ranging doctrinal consequences. Secular Buddhists de-emphasise traditional Buddhist theories of the world which seem to revolve around supernatural concepts such as karma, rebirth, saṃsāra and nirvāṇa, and focus on the experience of maintaining ethical and meditation practices.