the Earth’s spin axis has been wandering for at least the last five million years, ever since ice sheets began to build up in northern Canada and Scandinavia, When these ice sheets disappeared, they left behind a kind of depression in the Earth. “That's a mass deficit, with respect to the average Earth,” Ivins explains, “and it causes the pole to want to wander in the direction of that hole that's left there.” and there's more at: https://www.pri.org/stories/2016-05-04/melting-ice-causing-earths-axis-shift-direction OK Milankovitch cycles are variable?
Milankovitch cycles are generated from first principles, namely orbital mechanics and rigid body dynamics. They do not involve mass distribution changes in the planet itself, such as the melting of polar ice sheets.