Abstract We present 1.3 mm Atacama Large Millimeter/submillimeter Array observations of polarized dust emission toward the wide-binary protostellar system BHR 71 IRS1 and IRS2. IRS1 features what appears to be a natal, hourglass-shaped magnetic field. In contrast, IRS2 exhibits a magnetic field that has been affected by its bipolar outflow. Toward IRS2, the polarization is confined mainly to the outflow cavity walls. Along the northern edge of the redshifted outflow cavity of IRS2, the polarized emission is sandwiched between the outflow and a filament of cold, dense gas traced by N₂D⁺, toward which no dust polarization is detected. This suggests that the origin of the enhanced polarization in IRS2 is the irradiation of the outflow cavity walls, which enables the alignment of dust grains with respect to the magnetic field—but only to a depth of ∼300 au, beyond which the dust is cold and unpolarized. However, in order to align grains deep enough in the cavity walls, and to produce the high polarization fraction seen in IRS2, the aligning photons are likely to be in the mid- to far-infrared range, which suggests a degree of grain growth beyond what is typically expected in very young, Class 0 sources. Finally, toward IRS1 we see a narrow, linear feature with a high (10%–20%) polarization fraction and a well-ordered magnetic field that is not associated with the bipolar outflow cavity. We speculate that this feature may be a magnetized accretion streamer; however, this has yet to be confirmed by kinematic observations of dense-gas tracers.