Metasurfaces, two-dimensional (2D) or quasi-2D arrays of dielectric or metallic meta-atoms, offer a compact and novel platform to manipulate the amplitude, phase, and polarization of incoming wavefronts in a desired manner by engineering the geometry of meta-atoms. In polarization control, spin-insensitive metasurfaces have attracted significant attention due to the robustness of circular polarization against the beam misalignment and multi-path effects. Till now, several efforts have been made to realize polarization-insensitive metasurfaces for circularly polarized (CP) wavefront manipulation; however, these metasurfaces only consider the cross-polarization channels and keep the co-polarization channels abandoned. Such metasurfaces cannot be considered truly spin-insensitive, as one has to carefully choose the analyzer at output. Here, by combining the polarization-insensitive geometric phase and engineered propagation phase, we propose a spin-insensitive design principle based on metasurfaces that can perform identical functionality (on co- and cross-polarization channels) irrespective of the handedness of incident/transmitted light. As a proof of concept, we design and numerically realize two types of spin-insensitive wavefront engineering devices: (1) spin-insensitive meta-hologram and (2) spin-insensitive beam deflector with power splitting functionality. The proposed work is expected to open up new avenues for developing spin-independent metasurfaces-based devices.