Magnon-phonon hybridization provides a powerful route to couple spin and lattice excitations, yet the symmetry principle governing mode selectivity remains unclear. Here, we show that crystalline pseudoangular momentum provides a general criterion for selective magnon-phonon hybridization in noncollinear multisublattice magnetic systems. The rotation eigenvalue associated with pseudoangular momentum encodes polarization transformations, sublattice permutations, and Bloch phases, requiring magnetoelastic coupling between modes belonging to the same rotation sector. We illustrate this principle in a stacked kagome model with noncollinear spin order. An out-of-plane magnetic field tunes one magnon sector into resonance with a degenerate phonon doublet, yet only the pseudoangular-momentum-matched phonon develops a pronounced avoided crossing while the other remains nearly unmixed. Field reversal switches the selected rotation sector and reverses the rotational polarization of the hybridized phonon component without changing the hybrid-mode energies. Our results reveal pseudoangular-momentum matching as a general framework for understanding and controlling mode-selective spin-lattice hybridization.