This study investigates the effect of filament moisture content on material extrusion (MEX) 3D-printed composites using acrylonitrile butadiene styrene (ABS) as the polymer matrix and 0–10 vol% hexagonal boron nitride (BN) as reinforcement. ABS/BN composites were prepared through batchwise compounding and extruded into MEX-suitable filaments. The filaments were conditioned at 30 °C and 10% or 90% relative humidity (RH) before/during direct feeding into the 3D printer. Specimens were fabricated with raster angles parallel (0°) and perpendicular (90°) to their length. Micro- and macrostructural analyses using scanning electron microscopy and computed tomography revealed intensive void formation, especially in BN-filled composites 3D-printed from humid filaments. This was attributed to BN acting as a physical barrier, hindering the outgassing of evaporated water during 3D printing. Mechanical properties were evaluated using tensile and Charpy impact tests. Based on the tensile test results, neat ABS was the least sensitive to filament moisture, with tensile strength at 0° raster angle dropping from 40.5 MPa to 36.7 MPa as storage RH was increased from 10 to 90%. For composites with 10 vol% BN loading, tensile strength dropped from 34.1 MPa to 22.3 MPa. Charpy impact strength exhibited similar reductions, ascribed to the porous structure of the BN-filled composites caused by the evaporated moisture. Thermal conductivity was also examined, showing slightly superior performance for samples 3D-printed from filaments stored in less humid conditions. For unfilled ABS, the conductivity slightly decreased from 0.188 to 0.185 W/mK, while for 10 vol% BN-filled composite, it dropped from 0.778 to 0.617 W/mK.