Here's (from the first post in this thread) what I say about supermundane reality. I think this is sufficiently clear and circumscribed that it doesn't include non-religious
ideals for which people have fought and died, or non-religious 'non-material realities.' If you think otherwise, examples would help.

'I take it to be intuitive that religions are
concerned with a reality that surpasses the ordinary world that
sense perception reveals. This reality consists either of (a)
sentient supernatural beings (e.g. gods) or of (b) an insentient
metaphysical principle underlying the universe (e.g. The
Unconditioned, Sunyata, or The Tao). This principle has features
that mark it as belonging to a different order of reality from
the objects that make up the mundane world: it cannot be named or
cognized, it can be described only in contradictions, it doesn't
arise or pass away, it issues in everything else, it is utterly
changeless, or...

In short, religions relate practitioners to a reality that
transcends the mundane world revealed by sense perception; we
might call it a 'supermundane reality.' ...Even supposing we occasionally see
the gods walking among us, a significant part of their existence
must be unseen. (Indeed, the beings in question might better be
described as 'supermundane' than 'supernatural,' for the
practitioners may lack our concept of 'nature.') They reside
primarily on Mount Olympus or in a celestial realm. A 'god' who
rents the apartment next to mine, gets a job driving a bus, joins
the Libertarian Party, marries a coworker, and becomes completely
immersed in the mundane realm forever, is a theological oxymoron.
Similarly the insentient metaphysical principle must at least
partly transcend nature, even if we sometimes see its operations
in nature. It comprises a level of reality deeper than what sense
perception (even assisted by scientific instruments) reveals, and
its nature is best discovered by other means, e.g. meditation.

In addition,
the elements that comprise the reality to which a religion
relates us must be sufficiently grand (taken either individually
or collectively) that they can figure centrally in satisfying the
sort of substantial human needs that people generally want
religions to meet (e.g. long life, immortality, the end of
suffering). Gremlins do not a religion make. '