Abstract We investigate how self-interacting dark matter (SIDM) with anisotropic scattering affects the evolution of isolated dark matter haloes as well as systems with two colliding haloes. For isolated haloes, we find that the evolution can be adequately captured by treating the scattering as isotropic, as long as the isotropic cross-section is appropriately matched to the underlying anisotropic model. We find that this matching should not be done using the momentum transfer cross-section, as has been done previously. Matching should instead be performed via a modified momentum transfer cross-section that takes into account that dark matter particles can be relabelled after they scatter, without altering the dynamics. However, using cross-sections that are matched to give the same behaviour in isolated haloes, we find that treating dark matter scattering as isotropic underpredicts the effects of anisotropic dark matter scattering when haloes collide. In particular, the DM-galaxy offset induced by SIDM in colliding galaxy clusters is larger when we simulate the underlying particle model, than if we use a matched isotropic model. On the other hand, well-motivated particle models with anisotropic scattering typically have cross-sections with a strong velocity dependence, and we discover a previously unrecognised effect that suppresses DM-galaxy offsets in colliding clusters making it hard for these systems to provide competitive constraints on such particle models.