Or scope, if you prefer. Surely some sorts of problems are valid for soteriology to deal with, while others are not.
I prefer words! Abrangence is not an English word - I had first thought it was. Perhaps it should be.
For instance, some "problems" are simply too trivial for any religion to recognize as significant.
Maybe, but I think you'll find that those problems are subsets of problems that religion does consider significant; any kind of state which causes dissatisfaction for example. Take (y)our religion; Buddhism, duhkha. All transient states are viewed as ultimately dissatisfactory if perceived in their limited aspect by a falsely constru(ct)ed self-identifying process of awareness.
Simple things, like a broken shoelace, are symptomatic of duhkha and Buddhism consists of prescribing (and self-administering, as one would a medicine) means for non-apprehension of duhkha in all situations. For a religion to be truly universal, one might also argue, it must be applicable in all times, in all places, for all cognitive experience. Otherwise, where is its presence and practicality?
Others are just too obviously non-religious in nature: air pollution, for one.
Is this really obviously non-religious though? I'm also a Buddhist; though of a different stripe, and I work in environmental technology in large part because of my Buddhist religious beliefs. How do I get to environmental sentiments from Buddhism?
That Mahayana, the branch which I subscribe to (and perhaps you as well?), is built on two things; shunyavada (void wisdom) and karunopaya (compassionate method of endeavor).
The bodhisattva, while being cognitively inactive and ultimately actionless, non-conceptually selfless, viewing and reifying no particular constructed subrealities, dwelling instead in viewless, spaceless, timeless gnosis, simultaneously displays activity that seems intensely concerned with activity, self-experiences of other viewpoints encountering themselves reflected in conventional, constructed objects, and their relative suffering enmeshed in the illusion thereby created.
This, perhaps, presents the most interesting view of soteriology in the Dharmic traditions; interesting in that it's turned on its head. Rather than supplicating to saviors, aspirants are exhorted to offer themselves up on the altar of rebirth to bring about the salvation of all beings; each aspirant themselves a savior of others; indeed, saving them in large part by making them saviors themselves.
Someone correctly 'living' the mahayana ideal will experience deep love and compassion for everyone they may meet, cherishing them no less than their own self, intensely desirous of their well-being, and committed to the set of actions, words and thoughts most efficacious in bringing about better material and spiritual states for them.
The prajnaparamita sutra (the foundational text of the mahayana) says that whatsoever means for materially and spiritually bettering one's society should be implemented with full commitment and livelihood. Moreover, it doesn't draw the line at society, or humanity - it includes all beings in its scope, as its goal is explicitly the succor and enlightenment (absolute awareness & absence of suffering) of all beings.
And here's where I draw inspiration in my professional work; I view the imperative of mahayana - universal deliverance - as essentially a biotechnological problem in need of such a solution. This makes me a transhumanist abolitionist by virtue of only an interpretation informed by science and modern perspectives. So, if that's the solution to a sub-optimal state, what does our sub-optimal state consist of? Currently, life as we know it is facing extinction; 30,000 to 140,000 species go extinct per day, mostly as a result of human intervention in the biosphere. We're essentially dismantling our own life support system. Aside from the ecological issues, there are also enormous public health issues with pollution, and our industrial system itself suffers from resource unsustainability which is likely to destabilize the world economically, politically and militarily even irrespective of the environmental question altogether. What does this mean, from a mahayana perspective? These are all conditions that will bring about suffering and absence of awareness, and therefore must be avoided.
Leaving aside the problems for now, and considering the ethical ideal of mahayana viz. soteriology: if we can imagine a society where everyone, somehow, has been conditioned to live in this manner - active service for the sake of others, ceaseless expression of deliverance; what sort of world would we see? To most authentically live such a philosophy, one must commit one's professional skills and time to this method; one has to combine livelihood and 'spiritual work' here.
In the theme of this work, mahayana speaks of an economy of karmic merit which underlies the exchange of spiritual gifts and services; one is not supposed to identify with the merit itself, but 'reinvest' the 'revenue' continuously like breathing in and out, not least of which 'R&D expenses' in the meditative laboratory.
To return things to considering soteriology's appliance to Dharmic religions; is this not a most unique and remarkable brand of a soteriological doctrine - even if we do not agree with it?
It is simply not obvious (and IMO it is in fact quite arbitrary) whether there are any problems with religious significance that should or should not be considered as solvable by way of salvation. Is it salvation to, say, get a job in order to earn a salary and bring food to one's children? Is it religious practice?
In light of the above, is your opinion more open to the idea that, at least viewed from the perspective of a religion's adherents, it might well be?