Precession has affected weather a couple of ways. The first effect of the wobble is that about 8000 years ago the northern hemisphere received more sunlight. This in turn shifted the amount of rainfall which occurred in Africa. The second aspect is that during that time Earth was closest to the sun in the winter. Now it is closest during the summer. This article describes how a change in the "Hadley circulation" shifted with the end result of the Sahara turning to desert.

This phenomenon is actually known by scientists in the field. One problem with these other factors which are affecting climate is that they are a single news cycle event. Imagine if only precession was the cause (all the other factors were irrelevant). News broadcasters come on an say "Climate change is because of the wobble". There is no follow up to that item. People cannot change the wobble. You cannot raise money to fight the wobble etc.
Carbon caused climate change is something that can be spun out time and time again. I am perhaps being a little cynical but it is like investing in the stock market. When the bellboy has a hot tip ... its time to get out.