  We consider a 2d dipolar system, $d=2$, with the generalized dipole-dipole
interaction $\sim r^{-a}$, and the power $a$ controlled experimentally in
trapped-ion or Rydberg-atom systems via their interaction with cavity modes. We
focus on the dilute dipolar excitation case when the problem can be effectively
considered as single-particle with the interaction providing long-range
dipolar-like hopping. We show that the spatially homogeneous tilt $\beta$ of
the dipoles giving rise to the anisotropic dipole exchange leads to the
non-trivial reentrant localization beyond the locator expansion, $a<d$, unlike
the models with random dipole orientation. The Anderson transitions are found
to occur at the finite values of the tilt parameter $\beta = a$, $0<a<d$, and
$\beta = a/(a-d/2)$, $d/2<a<d$, showing the robustness of the localization at
small and large anisotropy values. Both extensive numerical calculations and
analytical methods show power-law localized eigenstates in the bulk of the
spectrum, obeying recently discovered duality $a\leftrightarrow 2d-a$ of their
spatial decay rate, on the localized side of the transition, $a>a_{AT}$. This
localization emerges due to the presence of the ergodic extended states at
either spectral edge, which constitute a zero fraction of states in the
thermodynamic limit, decaying though extremely slowly with the system size.
