About a decade ago, I read a novel about an Earth without a moon. It talked of a dimensional portal, where you could experience a series of situations (with and without moon) and how things changed with new conditions. It featured Neanderthals in the present day, although apprehensive of new technologies. There were modern matriarchal scientists who had gorilla like bodies to withstand the wind created by the rotation of the Earth without a moon, and who also acquired very long names. There were religious zealots (priests) with monkey tails.
It sounds like Stephen Baxter's "Origin", the third book in the Manifold Trilogy
- There are multiple alternate Earths, at least one without a moon
- There were some Homo Erectus and something like Neanderthals
- Hyper intelligent, matriarchal scientists from an Earth with very strong winds due to an extreme axial tilt