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.