This is just a spontaneous "knee-jerk" response with no evidence or expertise to back it up, but...
I recall hearing an account that the moon may be (at least in part) a portion of the earth that was knocked loose by an impact with some other large body during an early period in the solar system. If that's what happened, then the transfer of material from earth to moon is likely to have included some water, and depending on when that impact occurred, relative to the initial appearance of life on earth, the water may have contained some biotic material, which might have survived the event and the subsequent absence of atmosphere, ambient temperature, and other earth-specific properties.
Even if that turns out not to be a correct account of the moon's origin, it's still bound to be very enlightening to figure out the source that lunar water comes from, and it would be well worthwhile to look closely and see whether there's anything biological in that water.
If it contains no life, that's instructive in itself, and any non-religious perspective on the issue would be enriched by having this additional useful data, which leads to valuable subsequent questions, like "what, besides water, is needed for life?" Knowing what is present on earth but lacking on the moon will yield progress. (But obviously, the presence of life there would lead to a far more stimulating and challenging pursuit of the new questions this would raise.)
As for the impact of any sort of lunar life form on popular religious beliefs, well... believers will accommodate (or warp) the new facts and/or their existing theologies in order to arrive at some sort of amalgam -- or not -- the same as they would treat any other objectively established facts.
autotelic adj. (of an entity or event) having within itself the purpose of its existence or happening.
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