We determine the magnetic field strength in the OMC 1 region of the Orion A filament via a new implementation of the Chandrasekhar Fermi method using observations performed as part of the James Clerk Maxwell Telescope (JCMT) B-Fields In Star-forming Region Observations (BISTRO) survey with the POL-2 instrument. We combine BISTRO data with archival SCUBA-2 and HARP observations to find a plane-of-sky magnetic field strength in OMC 1 of ${B}_{athrm{pos } }=6.6m 4.7$ mG, where $elta {B}_{athrm{pos } }=4.7$ mG represents a predominantly systematic uncertainty. We develop a new method for measuring angular dispersion, analogous to unsharp masking. We find a magnetic energy density of $im 1.7imes {10}^{-7}$ J m-3 in OMC 1, comparable both to the gravitational potential energy density of OMC 1 (~10-7 J m-3) and to the energy density in the Orion BN/KL outflow (~10-7 J m-3). We find that neither the Alfvén velocity in OMC 1 nor the velocity of the super-Alfvénic outflow ejecta is sufficiently large for the BN/KL outflow to have caused large-scale distortion of the local magnetic field in the ~500 yr lifetime of the outflow. Hence, we propose that the hourglass field morphology in OMC 1 is caused by the distortion of a primordial cylindrically symmetric magnetic field by the gravitational fragmentation of the filament and/or the gravitational interaction of the BN/KL and S clumps. We find that OMC 1 is currently in or near magnetically supported equilibrium, and that the current large-scale morphology of the BN/KL outflow is regulated by the geometry of the magnetic field in OMC 1, and not vice versa.