After looking at the code cryosparc code of partice extraction, I agree that there is no need to flip the axes for the shiftx/shifty. Thank you for your clarification!
However, there still seems to be an issue when carrying out re-extraction in relion using exported cryosparc partices. Since the micrographs are y-flipped with respect to each other (cryosparc motion correction vs. motioncor2), the re-extracted particles would be y-flipped as well even though the centering is accurate. That y-flip or mirroring along the x-axis would probably require modifications of the Euler angles (my guess is (180+φ, 180-θ, -ψ) according to the 3DEM convention).
cryosparc particles (left) vs re-extracted particles(right)
