So really my posts were more about finding situations where arbitrary beliefs may be demonstrated or suggested to be useful, as a counterpoint to our earlier discussions where you posited that arbitrary beliefs were almost always not useful.

I am not intending to imply that religion is a human creation, but it is easy to draw that inference from what I have said and I have done nothing to suggest otherwise.
On a theological note where the ‘object’ of religious belief and practise is ‘other’ it is perhaps inevitable that religious practise is man-made.
A theological speculation may ask “if nobody worships him does God cease to exist?”…
sounds similar to “what sound does a falling tree make in a forest when there is nobody there to hear it?”
This is a pertinent question that can be re-written back to me as:- “as nobody worships the ancient gods of the roman pantheon have they ceased to exist?”
The only speculative answers I could give to these speculative questions concern archetypes and the human myth-making faculty that perhaps anthropromorphises a deistic principle into God, or perhaps de-constructs a spiritiually abstract archetype into many lesser specific archetypes, the mother, the father, the son, the creator and so on.

I disagree however also with the notion that truth has nothing to do with arbitrary belief, be it sport, imaginary friends or God.
I will consider just two of many possibilities here.
1) sport and imaginary friends will necessarily use archetypal images with which we are familiar. In sport the hero figure, or the warrior, or the combat between two forces are obvious archetypal images that reflect reality (either as it is now, or as it once was). This reality is deeply imprinted on the human psyche. Imaginary friends may take the form of fictional film or book characters, they may be a combination of many real or fictional characters, they may even be completely imaginary. They may be nonsense anthropromorphic entities such as a talking animal, or as a living breathing cuddly toy and teddy bear. However it manifests itself the imaginary friend just like the different psychological dynamics involved in sport will necessarily reflect ‘aspects’ of reality.
One may take the imaginary friend perhaps as a simile for religious beings, Jesus as man-God, Avalokiteśvara the Buddha of compassion, Krishna the cowherd. Perhaps these figures part real part imaginary have been manifestations of archetypes and reflections of reality. But that is for another discussion.
2) Arbitrary belief, is defined by your criteria as unjustified and based on a lack of empirical and observational evidence. I hate to ressurect the language games hypotheses but one area where arbitrary belief is pertinent is in internal intuitions. These are by definition impossible to be empirically tested or to be observed. Likewise my dreams, my visions, my hallucinations and my perceptions of reality. To return to the brain in the vat and the solipsistic skeptic are not all my beliefs arbitrary?
Now then we should give some credence to the idea that not all is an illusion and that there is a shared reality in which we participate, but this shared reality is limited and we are often unable to objectively experience the reality of others, i.e. my pain. You can only know of it through my reporting it, through observing various signs that suggest I am in pain, and perhaps through measuring electronic impulses in the brain, but you do not know IT.
I am leading, rather laboriously to the idea of religious experience, mystical experience and the ineffable experiences. I can only recommend a look at the ideas of Rudolf Otto and William James on religious experience, otherwise this overlong post will get even larger.
What I ask is: by what legitimate skeptical authority can you an external observer pass valid judgement* on the internal experiences of my mind that I have a sense, intuition, or feeling of being real or truthful?

* we can assume that I am not manifesting signs of mental illness.

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