What about these (normal small perturbations in orbital angles) effects on spinning tops that are well known for decades affect Earth's climate/weather?
I haven't seen that discussed in the global climate change documentaries.
A possible reason that you haven't seen it is probably because popular media reporting of anything technical is usually risible. At best incomplete. Which is a reason why many of these popular online discussions rarely rise above the level of noise. It is commonplace for people without much specific technical knowledge to have an idea or to read something on a subject and ask why this wasn't known, much as you have done above. However, these things ARE well-known, part of the basic body of knowledge in a field, but not something that's discussed much because there is no reason to. Architects don't refer to Newton's third law when being interviewed about a newly designed building.
It's not logical to assume that the thousands of researchers in the field of climate science don't know about orbital nutation or what effect they might possibly have? It's more sensible to assume that you simply don't know about it because it's not your field. I suspect that if you start digging, you'll find mountains of research in that area and that it has been incorporated into the various climate models for a long time now. If it hasn't been discussed in popular forums, it might be because people instead waste their time arguing that CO2 is a fertilizer.
https://en.wikipedia.org/wiki/Nutation Thousands of researchers around the world spend years of detailed study in all aspects of the related sciences that affect climate, physics, chemistry, biochemistry, etc. It is not logical to assume that concepts that emerge in online public discussions such as this one have not been thought of by them. I would say that it is inconceivable. The average non-scientist citizen does not have the time to read the one-paragraph abstracts of all the research articles written in a year, never mind digest all the content. And that's just the English language articles.
Before retirement, my day job was copy-editing physics and chemistry journals (my background was in physics but that was a lifetime ago), and we used to receive submissions from cranks all the time. There are not enough hours in the day to respond to them, and anyway it's a waste of time. I read 10 pages once on why Einstein was wrong about relativity, great laugh over lunch. I suspect that medical journals get submissions from people who try to deny the germ theory of disease. It's an occupational hazard.
If you want to delve into these matters more deeply, my advice would be to start with journals like Science, New Scientist, Scientific American, etc., not online discussions where it is not possible to determine the credentials of the contributors. The articles in those journals will all have extensive bibliographies into which you could dive.
I did not intend to go on at length. it's just that there are literally thousands of scientific journals with dozens of articles written for every issue, and it makes no sense to seek info about those topics from daily newspapers or photographic web sites.