@neologist,
There are a lot of connotations to the word, but I don't see a problem with 'indiscriminate' or 'haphazard.' Very young children, to my knowledge, generally lack the cognitive skills needed to discriminate between evidence-based, falsifiable claims and evidence-free, unfalsifiable faith-based ones. As for 'haphazard,' I think that fits, too. Kids tend to just say the first idea that pops into their heads, regardless if it contradicts something else they said earlier.
Anyway, the word 'innate' doesn't help very much. You fall prone to the naturalistic fallacy if you go in that direction. In any event, I don't see any way that it would help support the god hypothesis.