I'm not sure if there is a positive answer, let alone an objective one, because a self-proclaimed "sbnr" person might be a non-denominational theists or a committed materialists who waxes lyrical about the grandeur of the universe (like Dawkins1), but I'll try.
In my view, it would be dualism in a very broad sense, or better non-materialism. Also, pan(en)theism seems to be closely tied to sbnrness.
In more traditionally religious countries, non-denominational belief in God (theistic or deistic) or in karma and reincarnation may be seen as spiritual and not as religious. For example the astronaut Gene Cernan says in the documentary In the Shadow of the Moon:
I felt that the world was just too beautiful to have happened by accident. There has to be something bigger than you and bigger than me. And I mean this in a spiritual sense, not a religious sense. There has to be a creator of the universe who stands above the religions that we ourselves create to govern our lives.
On the other hand, I believe that "spiritual materialism (physicalism)" rests on a confusion. If we accept materialism, we have broadly two options.
we consistently see humans as products and part of this
value-free, purposeless universe, as biological robots, like Alex
Rosenberg2, and end up with an undisguised nihilism. It is not clear how we can free ourselves from what a dysteleological evolution imprinted in us. And even if that would be possible, evolution may still actively act against our "noble motives".
we accept an unexplainable gap, which separates a
fundamentally different human sphere of value, purpose and
qualitative experience (like feelings, sound, color etc.) from the barren rest of the universe, only governed by
purposeless mathematical laws3. Imho because of this gap, this is an absurd and incoherent view. But more importantly, it is pretty nihilistic too, because it severely alienates humanity from the rest of nature.
So it seems clear to me, that materialism because of its nihilistic implications is incompatible with anything that can justifiably be called spirituality.
though what Dawkins describes as "grandeur" and "beauty", to me just seems the unimaginably hugeness, complexity and scariness of the universe.
2 Alex Rosenberg: "The Atheist's Guide to Reality: Enjoying Life without Illusions"
3 for example, see
Richard Dawkins & Steven Pinker: "Is science killing the soul?", Edge 1999