Therefore anatta has no bearing on the question "should we believe in post-mortem rebirth?"
Should we believe in post-mortem rebirth???
Super mundane practice has very little or no place for beliefs. Beliefs are for morality and the mundane cultivations. Thus, Buddhists "beliefs" and Hindu/christian beliefs all have a common cause. IMO, one is no better than the other.
While it is true that we need to answer the OP's question, I think it makes sense to at least nudge them in the right direction if possible. Stating unverifiable beliefs as ultimate truths and presenting them as "Buddha taught" can be misleading. It makes sense to direct them to things they can observe and verify for themselves here and now. It is important for a beginner to establish some amount of faith in the Dhamma by direct observation of what the Buddha has taught to be applied moment to moment. When a beginner asks about a belief in the forum and we answer with more belief theories, what difference would it make? Not much