As the ocean tide flows over the rough seafloor, it induces topographic stresses that feed back on the strength of the tide. Here, we examine how these topographic stresses change as the dynamical regime transitions from barotropic to baroclinic with increasing stratification and/or decreasing topographic length scale, thereby bridging between previous work which studied one or other regime in isolation. Our investigation is conducted using linear theory validated by comparison with a suite of over 100 fully nonlinear numerical simulations. For superinertial tidal flows across an isolated ridge, it is shown that the topographic stress rapidly transitions from out of phase with the tidal flow to in phase with the tidal flow at ridge widths of 1–2 times the baroclinic mode-1 wavelength. This change in stress is associated with a switch from topographically confined perturbation flows in the barotropic regime to radiating waves in the baroclinic regime. The transition becomes more complicated in the presence of multiple ridges due to the interference of the waves generated at each. These interactions lead to significant changes in both the magnitude and phase of the topographic stress as compared to the sum of the contributions from two isolated ridges. Further, particular combinations of ridges—so-called “invisible topographies”—lead to exactly zero stress and, therefore, have no effect on the barotropic tide. These results have implications for improving models of ocean tides and tidally driven mixing.