Hi everyone,
First, a disclaimer: I know that TEME is not a recommended frame (lack of common definition, pointed out by CCSDS for example and well traced in Orekit’s documentation) and should be avoided, but unfortunately some data e.g. 18SDS’s SP ephemerides do come in that frame.
I have made a simple test which is the following (code follows):

I create an instance of
EquinoctialOrbit
from a GCRF positionvelocity vector. 
I propagate it for 3600s as is with a
KeplerianPropagator
and store the result 
I take the original orbit, convert it into TEME, propagate in to the same date in Keplerian motion again and convert back to GCRF. I get differences almost of the order of a meter!
// Initial date in UTC time scale
final TimeScale utc = TimeScalesFactory.getUTC();
final AbsoluteDate initialDate = new AbsoluteDate(2021, 10, 2, 0, 0, 0.000, utc);
// Frames
final Frame inertialFrame = FramesFactory.getGCRF();
final Frame teme = FramesFactory.getTEME();
// Initial conditions
final double r0 = Constants.WGS84_EARTH_EQUATORIAL_RADIUS + 500e3;
final double v0 = FastMath.sqrt(Constants.WGS84_EARTH_MU / r0);
final double mass = 10.;
final Vector3D pos = new Vector3D(r0, 0., 0.);
final Vector3D vel = new Vector3D(0., v0, 0.);
final PVCoordinates pv = new PVCoordinates(pos, vel);
final double mu = Constants.EGM96_EARTH_MU;
final EquinoctialOrbit orbit = new EquinoctialOrbit(pv, inertialFrame, initialDate, mu);
final SpacecraftState state = new SpacecraftState(orbit, mass);
// Propagate in original frame
final double dt = 3600.;
final AbsoluteDate date = initialDate.shiftedBy(dt);
final KeplerianPropagator prop1 = new KeplerianPropagator(orbit, mu);
final PVCoordinates pvProp = prop1.propagate(date).getPVCoordinates(inertialFrame);
// Convert in TEME, propagate and convert back
final EquinoctialOrbit orbitTransfo = new EquinoctialOrbit(state.getPVCoordinates(teme), teme, initialDate, mu);
final KeplerianPropagator prop2 = new KeplerianPropagator(orbitTransfo, mu);
final PVCoordinates pvProp2 = prop2.propagate(date).getPVCoordinates(inertialFrame);
final double[] diffPos = (pvProp.getPosition().subtract(pvProp2.getPosition())).toArray();
final double[] diffVel = (pvProp.getVelocity().subtract(pvProp2.getVelocity())).toArray();
I am a bit surprised, TEME is still supposed to be pseudoinertial no? How can I have such big differences in such short time? Please point out any mistakes I have made.
Cheers,
Romain.