Switchable Anomalous Hall Effects in Polar-Stacked 2D Antiferromagnet MnBi₂Te₄

van der Waals (vdW) assembly of two-dimensional (2D) materials allows polar layer stacking to realize novel properties switchable by the induced electric polarization. Here, based on symmetry analyses and density-functional calculations, we explore the emergence of the anomalous Hall effect (AHE) in antiferromagnetic MnBi₂Te₄ films assembled by polar layer stacking. We demonstrate that breaking P̂T̂ symmetry in an MnBi₂Te₄ bilayer produces a magnetoelectric effect and a spontaneous AHE switchable by electric polarization. We find that reversible polarization at one of the interfaces in a three-layer MnBi₂Te₄ film drives a metal-insulator transition, as well as switching between the AHE and quantum AHE (QAHE). Finally, we predict that engineering interlayer polarization in a three-layer MnBi₂Te₄ film allows converting MnBi₂Te₄ from a trivial insulator to a Chern insulator. Overall, our work emphasizes the topological properties in 2D vdW antiferromagnets induced by polar layer stacking, which do not exist in a bulk material.