Twisting van der Waals bilayers creates a moir'e stacking field with periodically varying local interlayer registry, enabling spatially patterned polarization. However, a systematic understanding of how this registry-controlled polar topology evolves with twist angle, temperature, and mechanical strain is still lacking. Here, using first-principles-trained deep-potential molecular dynamics simulations, we show that spatially varying interlayer registry governs the polarization texture and can be directly tuned by twist and relative layer deformation. As the twist angle decreases, the moir'e polarization texture evolves from compact, nearly circular vortex-like patterns to extended triangular AB/BA domains. This crossover arises from enhanced lattice relaxation at small twist angles, which expands low-energy, oppositely polarized AB/BA regions and confines in-plane polarization mainly to domain boundaries. Despite this reconstruction, the local in-plane winding remains tied to interlayer registry and persists up to 1000 K, indicating robust topology against thermal fluctuations. We further show that the mechanical response is dictated by whether deformation changes the relative registry: homogeneous deformation of both layers produces only weak distortions, whereas layer-selective deformation strongly reconstructs the moiré polarization texture. A mismatch-matrix registry-mapping model is developed to capture this response, explaining deformation-induced changes in vortex radii at larger twist angles and triangular-domain geometry at smaller twist angles. These results identify interlayer registry as the central control parameter for forming and tuning moir'e polar topology in twisted bilayer h-BN.