In the Solar System, about 98% of this effect is contributed by the orbital angular momenta of the four giant planets (Jupiter, Saturn, Uranus, and Neptune).
The orbital angular momenta of the Sun and all non-jovian planets, moons, and small Solar System bodies, as well as the axial rotation momenta of all bodies, including the Sun, total only about 2%.
If all Solar System bodies were point masses, or were rigid bodies having spherically symmetric mass distributions, and further if there were no external effects due to the uneven gravitation of the Milky Way Galaxy, then an invariable plane defined on orbits alone would be truly invariable and would constitute an inertial frame of reference.
But almost all are not, allowing the transfer of a very small amount of momenta from axial rotations to orbital revolutions due to tidal friction and to bodies being non-spherical.
Nevertheless, these changes are exceedingly small compared to the total angular momentum of the system, which is very nearly conserved despite these effects.
For almost all purposes, the plane defined from the giant planets' orbits alone can be considered invariable when working in Newtonian dynamics, by also ignoring the even tinier amounts of angular momentum ejected in material and gravitational waves leaving the Solar System, and the extremely tiny torques exerted on the Solar System by other stars passing nearby, Milky Way galactic tides, etc.