The emerging meta-holograms rely on arrays of intractable meta-atoms with various geometries and sizes for customized phase profiles that can precisely modulate the phase of a wavefront at an optimal incident angle for given wavelengths. The stringent and band-limited angle tolerance remains a fundamental obstacle for their practical application, in addition to high fabrication precision demands. Utilizing a different design principle, we determined that facile metagrating holograms based on extraordinary optical diffraction can allow the molding of arbitrary wavefronts with extreme angle tolerances (near-grazing incidence) in the visible–near-infrared regime. By modulating the displacements between uniformly sized meta-atoms rather than the geometrical parameters, the metagratings produce a robust detour phase profile that is irrespective of the wavelength or incident angle. The demonstration of high-fidelity meta-holograms and in-site polarization multiplexing significantly simplifies the metasurface design and lowers the fabrication demand, thereby opening new routes for flat optics with high performances and improved practicality.