Long-range correlated motions couple distant protein regions, supporting allosteric communication, cooperative conformational change, and the balance between structural stability and sensitivity. Yet whether this scale-free coordination persists under the directional constraints of a lipid bilayer, and how it is reorganized, remains unclear. Using an implicit-membrane anisotropic network model, we analyze experimentally resolved $\alpha$-helical and $\beta$-barrel membrane proteins and extend the analysis to more than 3,000 human transmembrane proteins. We find that membrane anisotropy breaks the directional symmetry of long-range correlations without destroying their scale-free organization. Across protein sizes and topologies, the correlation lengths continue to scale with the corresponding molecular dimensions, while increasing anisotropy extends in-plane correlations and shortens those along the membrane normal. Because spontaneous correlations and perturbation responses share the same underlying mechanics, we further resolve residue-level responses into in-plane and normal components. The resulting directional mechanical susceptibility reveals mutation-sensitive sites in GPCRs beyond those prioritized by conventional scalar flexibility measures. Together, these results connect membrane-induced symmetry breaking of collective protein dynamics to direction-specific, residue-level functional sensitivity.