The Milankovic Solar Cycles explain a lot about long term climate changes. They don't explain it all in my opinion. From 400k years ago to 800k years ago, I would have been perfectly content with the Milankovic explanation of glacial periods.
From 400k years to now, I would not be so convinced. There is an odd change in the relationships that I have never heard a complete explanation that didn't require some hand waving.
It appears to be a long term change.
Like something not related to the sun is changing. What could it be?
The red hair step child of Milankovic Cycles, precession. The vertical x-axis lines are set at 23,000 years. Currently, Astral summer has higher solar insolation that NH summer by about 40Wm-2. Since that is a season fluctuation, the annual average, 1361Wm-2 is the forcing value used. Where forcing is applied is just as important as the amount of forcing. With the Southern Hemisphere toward the sun, the oceans, mainly in the southern hemisphere, can absorb more energy. The oceans though are not an infinite reservoir. They are limited by atmosphere and the saturation pressure of the primary Greenhouse gas, water vapor. When precession is synchronize with other orbital forcings and a mean ocean heat capacity, the forcings have a more dramatic impact than when out of phase. When precession is in phase with a rising ocean heat capacity, which can happen when polar ice extent reduces polar heat loss, then precession alone can have an impressive impact. The optimum flow of the Antarctic Circumpolar Current with average or above surface wind and sea ice extent allow for more than adequate cooling of the southern oceans. More than adequate equates to internal, natural variations in ocean heat content. UPDATED Chart:
That is the precession based on the 65N spreadsheet from the WUWT, "Onset of the Next Glaciation", post so it should be tweaked, but the period should be in the ballpark.