*

Dirac magnon system CrI₃ with a honeycomb lattice is a potential host of topological edge magnons. It ideally orders ferromagnetically (FM) (T_c=61 K) on cooling to the rhombohedral (R) phase, but antiferromagnetic (AFM) order has been detected in nanometer thin flakes, attributed to monoclinic (M) layer stacking which is the high temperature phase. Using a powder sample in which the sliding transition to the R-phase was largely inhibited (2:1 M:R ratio), clear evidence for M-type AFM order (T_N=50 K) coexisting with R-type FM order is observed in the bulk. From inelastic neutron scattering, a lower magnon energy is observed compared to the R phase, consistent with smaller interlayer interactions expected in the M phase. Notably, both the R and M phases have Dirac gaps. While a gap at the Dirac points has been reported in the R phase, the gap is clearly observed even when the majority is M-type as in our sample, suggesting that the same nontrivial magnon topology of the R phase is present in the M phase as well.