Persistent motion is ubiquitous in nature, for example in turbulence, active matter and movement of animals. In a persistent motion, the moving object prefers to continue moving in the same direction, while in an anti-persistent motion it prefers to backtrack. The effects of persistence, and history-dependent motion in general, on the behaviour of a single random walker are well known and have been thoroughly investigated. In general, the mobility of a single persistent walker is large compared to that of an anti-persistent walker. We consider a simple model of interacting persistent walkers on a lattice, and investigate the combined effect of the persistence and the volume exclusion interaction. By considering the hydrodynamic limit of this model, we find that the persistent-induced correction to the effective diffusion coefficient is positive for either persistent walkers at low density or anti-persistent walkers at high density, and negative otherwise. This means that at high enough density, the mobility of anti-persistent walkers is higher than that of persistent-walkers, in stark contrast to the behaviour of single walkers.