hBN alignment orientation controls moir\'e strength in rhombohedral graphene

Rhombohedral multilayer graphene hosts a rich landscape of correlated symmetry-broken phases, driven by strong interactions from its flat band edges. Aligning to hexagonal boron nitride (hBN) creates a moir\'e pattern, leading to recent observations of exotic ground states such as integer and fractional quantum anomalous Hall effects. Here, we show that the moir\'e effects and resulting correlated phase diagrams are critically influenced by a previously underestimated structural choice: the hBN alignment orientation. This binary parameter distinguishes between configurations where the rhombohedral graphene and hBN lattices are aligned near 0{\deg} or 180{\deg}, a distinction that arises only because both materials break inversion symmetry. Although the two orientations produce the same moir\'e wavelength, we find their distinct local stacking configurations result in markedly different moir\'e potential strengths. Using low-temperature transport and scanning SQUID-on-tip magnetometry, we compare nearly identical devices that differ only in alignment orientation and observe sharply contrasting sequences of symmetry-broken states. Theoretical analysis reveals a simple mechanism based on lattice relaxation and the atomic-scale electronic structure of rhombohedral graphene, supported by detailed modeling. These findings establish hBN alignment orientation as a key control parameter in moir\'e-engineered graphene systems and provide a framework for interpreting both prior and future experiments.