> The orbital period (the length of a sidereal year) is also invariant, because according to Kepler's third law, it is determined by the semi-major axis.
Which makes sense, because the semi-major axis depends on the energy of the orbit, and there's not really much that would be altering that in the short timeframe of a Milankovitch cycle.
It should be mostly invariant, but tugs and changes from other bodies in the system (Jupiter and Saturn particularly) can change the energy of the orbit. It's one of things that makes n-Body solutions to orbital mechanics nearly impossible to make. I doubt it's change too significantly for something as massive as earth though, but the collision with the mars sized body that created the moon early on in Earth's history definitely would have been able to change the orbital energy.
Kepler's law is an approximation, and it most certainly does not hold over large time scales. Heck, it fails on short time frames too - one of the early successes of relativity was to explain the precession of Mercury's perihelion from Kepler style theory to observation.
Heck, even restricting to classical physics, Kepler's law fails as soon as you have three bodies, since the derivation is only for a two body problem. A third (or more) body makes his laws fail. Our solar system has well over thousands of bodies all interacting.
So this is only an argument for the invariance of the (incomplete) model of Kepler, but fails in real life. We have plenty of better models (i.e., that agree better with observation) that are not invariant.
> The orbital period (the length of a sidereal year) is also invariant, because according to Kepler's third law, it is determined by the semi-major axis.
Which makes sense, because the semi-major axis depends on the energy of the orbit, and there's not really much that would be altering that in the short timeframe of a Milankovitch cycle.