Dependence of the DM-galaxy (upper row) and DM-BCG (lower row) offsets on the amount of anisotropy of the differential cross section dσ/dΩ while keeping the viscosity cross section σ_V/m_χ = 1 cm² g⁻¹ fixed. We show results obtained within the hSIDM scheme, assuming the ‘Møller’ cross section Eq. (1) with various values of the anisotropy parameter r (see Eq. (3)) related to the ratio of mediator and DM particle masses. For comparison, we also show the cases of purely forward-dominated scattering (fSIDM) and isotropic scattering (isotropic rSIDM), respectively. The left column shows the time evolution, the right column the maximal absolute offsets within t ∈ [1.5 Gyr, 3 Gyr]. The maximal offsets for models with realistic angle dependence approach those for purely forward-dominated scattering for r ≳ 10² (corresponding to m_ϕ/m_χ ≲ 0.1v/c, where v is the typical velocity scale), and those for isotropic scattering for r ≲ 1 (m_ϕ/m_χ ≳ v/c). The error bars and error bands are computed following Fischer et al. (2021b).