It's called Draysonian precession, and it's more akin to the 90* off motion of a disturbed gyroscope than a wobbling top. The moon is actually a stabililizing force, not the destabilizing one. Without the moon, the earths wobble would be massively worse, and the planet would most likely be uninhabitable. I'm talking about the poles pointing at the sun and every other inclination possible.

While there may be some effect on global warming, if global warming is real at all, and not just normal temperature fluctuation, I bet it's miniscule.

There are two real sources of earth atmosphere heating, sun radiant heating and fossil core heat getting to the surface. The sun is vastly predominant. Olber's paradox suggests another source, but I believe it's been debunked.

And as a final note, the belief in natal horological astrology almost precludes any internalized knowledge of science on the part of the believer. Therefore, the scientific inconsistency of astrologers is moot...