If an orbit is shifting due to orbital precession, is it still a Keplerian orbit? I was thinking about orbits a few days ago, and realized that orbits shift/precess naturally. Given that a two-body problem with a star and a planet, if the planet has an eccentric orbit that precesses, would we still call it a Keplerian orbit?
No orbits are strictly Keplerian, unless you really monkey about with your coordinate systems. However, a precessing orbit is pretty darned Keplerian.

The relationship between the various orbital elements can be a little complicated, and precession is traditionally thought of as the rotation of the periapsis of the orbit around the more massive body.  If we look at the orbital elements, we can think of it instead as a changing term to the longitude of the ascending node.  So we could capture the longitude of the ascending node, $\Omega_0$ at some initial time $t_0$.  Then, at any time t, the longitude of the ascending node would be $\Omega=\Omega_0+(t-t_0)\omega_p$, where $\omega_p$ is the rate of precession.  The rest of the orbital elements can be treated as constant.