We investigate the ability of state-of-the-art redshift-space distortion models for the galaxy anisotropic two-point correlation function, ξ(r⊥, r∥), to recover precise and unbiased estimates of the linear growth rate of structure f, when applied to catalogues of galaxies characterized by a realistic bias relation. To this aim, we make use of a set of simulated catalogues at z = 0.1 and 1 with different luminosity thresholds, obtained by populating dark matter haloes from a large N-body simulation using halo occupation prescriptions. We examine the most recent developments in redshift-space distortion modelling, which account for non-linearities on both small and intermediate scales produced, respectively, by randomized motions in virialized structures and non-linear coupling between the density and velocity fields. We consider the possibility of including the linear component of galaxy bias as a free parameter and directly estimate the growth rate of structure f. Results are compared to those obtained using the standard dispersion model, over different ranges of scales. We find that the model of Taruya et al., the most sophisticated one considered in this analysis, provides in general the most unbiased estimates of the growth rate of structure, with systematic errors within ±4 per cent over a wide range of galaxy populations spanning luminosities between L > L* and L > 3L*. The scale dependence of galaxy bias plays a role on recovering unbiased estimates of f when fitting quasi-non-linear scales. Its effect is particularly severe for most luminous galaxies, for which systematic effects in the modelling might be more difficult to mitigate and have to be further investigated. Finally, we also test the impact of neglecting the presence of non-negligible velocity bias with respect to mass in the galaxy catalogues. This can produce an additional systematic error of the order of 1–3 per cent depending on the redshift, comparable to the statistical errors the we aim at achieving with future high-precision surveys such as Euclid.