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When hexagonal boron nitride (hBN) and graphene are aligned at zero or smalltwist angle, a moir\'e structure is formed due to the small lattice constantmismatch between the two structures. In this work, we analyze magnetic orderingtendencies, driven by onsite Coulomb interactions, of encapsulated bilayergraphene (BG) forming a moir\'e structure with one (hBN-BG) or both hBN layers(hBN-BG-hBN), using the random phase approximation. The calculations areperformed in a fully atomistic Hubbard model that takes into account all$\pi$-electrons of the carbon atoms in one moir\'e unit cell. We analyze thecharge neutral case and find that the dominant magnetic ordering instability isuniformly antiferromagnetic. Furthermore, at low temperatures, the criticalHubbard interaction $U_c$ required to induce magnetic order is slightly largerin those systems where the moir\'e structure has caused a band gap opening inthe non-interacting picture, although the difference is less than 6%.Mean-field calculations are employed to estimate how such aninteraction-induced magnetic order may change the observable single-particlegap sizes.

Magnetic ordering tendencies in hexagonal boron nitride-bilayer graphene moir\'e structures