Microorganisms often move in confined, disordered environments, where hydrodynamic couplings can modify their transport behavior. Using extensive finite-element simulations, we investigate the dynamics of microswimmers – modeled as squirmers – in two-dimensional disordered porous media by resolving the full hydrodynamic interactions. We reveal that the deterministic coupling between activity, hydrodynamics, and disorder is sufficient to generate effective diffusive transport. Strong pushers and pullers become localized in the porous medium either by trapping at corners or dynamic trapping, depending on swimmer type and the obstacle packing fraction. Squirmers can escape from dynamic traps, leading to prominent “hop-and-trap'' dynamics. Strikingly, we find a pusher-puller asymmetry in the trapping probability that can be reversed by short-range swimmer–obstacle interactions, highlighting the sensitivity of transport to near-field effects.