We present a comprehensive theoretical investigation of the magnetic moments of open heavy-flavor molecular pentaquarks with quark compositions bc̄qqq and cb̄qqq (where q=u,d,s). Employing a molecular picture in which the pentaquarks are treated as S-wave bound states of a heavy baryon and a meson, we systematically construct the complete spin–flavor wavefunctions for the two distinct SU(3)_f octet representations, 8_1f and 8_2f, arising from symmetric and antisymmetric light-diquark configurations, respectively. Within the framework of the constituent quark model, we calculate the magnetic moments of spin-parity configurations, J^P = 1/2⁻(1/2⁺⊗ 0⁻) and J^P = 1/2⁻, 3/2⁻(1/2⁺⊗ 1⁻), for each member of the bc̄ and cb̄ octets. Our results reveal a striking hierarchy: in the 8_2f representation, the 1/2⁺⊗ 0⁻ states exhibit near-universal magnetic moments (μ ≈ -0.062 μ_N for bc̄qqq and μ ≈ +0.362 μ_N for cb̄qqq), as a direct consequence of the spin-singlet light-diquark that suppresses light-quark contributions. In contrast, the 8_1f representation shows a broad spectrum of values with frequent sign changes, reflecting the active role of the symmetric light-diquark. The clear differences between the bc̄ and cb̄ families demonstrate explicit heavy-quark flavor symmetry breaking in electromagnetic observables. These predictions provide a detailed set of electromagnetic benchmarks that can serve as discriminants for the internal flavor structure and spin configuration of future experimentally observed open heavy-flavor pentaquarks, offering valuable guidance for ongoing and future searches at facilities such as LHCb and Belle II.