Full Poincaré beams, as a more complicated class of novel structural beams, lead to impressive demonstrations recently in Free-Space Optical Communication (FSOC) due to the coupling of spin and orbital angular momentum in the cross section. However, a noteworthy limiting factor of FSOC system in this process is the varying atmospheric turbulence which results in beam expansion, drift, light intensity scintillation and other severe effects. Massive numerical simulations on turbulent atmospheric propagation of full Poincaré beams with C-point polarization, cylindrical vector beams with V-point polarization and homogeneous scalar polarized vortex beams through random phase screens were demonstrated. In this process, normalized correlation coefficient and mode purity were proposed to explore the robustness of full Poincaré beams on different locations of hybrid-order Poincaré sphere. The results show that full Poincaré beams with coordinates located in the southern hemisphere remain high robustness under weak and moderate turbulence (r₀=0.5 m, 0.125 m) compared with cylindrical vector beams and scalar vortex beams with similar topological charges and intensity distribution. While the dominant area shrinks to 2σ∈[-5π/32, 0] (latitude coordinates) under strong turbulence (r₀=0.056 m). These results will promote the selection of robust transmission media and the development of transmission quality in free-space communications with long-distance.