Let's contrive an example: If everyone abandoned the cause 'prevent global warming over the time scale of 30 years' it would still be less of a lost cause than the cause "raise this child with faith in God such that she is accepted into eternal life in heaven" even though there may be several people diligently and actively working toward said cause.

First, you haven't supported your first statement at all - if everyone stopped trying to prevent global warming, what is the probability of successfully preventing global warming? Global warming could be averted by events such as a supervolcano or comet impact, but "preventing global warming" is a subgoal of "preserve the environment" or "reduce existential risk" so such disasters would not really count as accomplishing the task.

Second, if your mission is to raise a child that is accepted into heaven, it could be successful if somebody creates an AI which simulates the Christian God and uploads dead people into simulated realities in engineered basement universes or something.