We study the phase diagram of the interacting two-dimensional electron gas (2DEG) with equal Rashba and Dresselhaus spin-orbit coupling, which for weak coupling gives rise to the well-known persistent spin-helix phase. We construct the full Hartree-Fock phase diagram using a classical Monte Carlo method analogous to that used in Phys. Rev. B 96, 235425 (2017)10.1103/PhysRevB.96.235425. For the 2DEG with only Rashba spin-orbit coupling, it was found that at intermediate values of the Wigner-Seitz radius rs the system is characterized by a single Fermi surface with an out-of-plane spin polarization, whereas at slightly larger values of rs it undergoes a transition to a state with a shifted Fermi surface and an in-plane spin polarization. The various phase transitions are first order, and this shows up in discontinuities in the conductivity, and the appearance of anisotropic resistance in the in-plane polarized phase. In this paper we show that the out-of-plane spin-polarized region shrinks as the strength of the Dresselhaus spin-orbit interaction increases and entirely vanishes when the Rashba and Dresselhaus spin-orbit coupling strengths are equal. At this point the system can be mapped onto a 2DEG without spin-orbit coupling, and this transformation reveals the existence of an in-plane spin-polarized phase with a single displaced Fermi surface beyond rs>2.01. This is confirmed by classical Monte Carlo simulations. We discuss experimental observation and useful applications of the novel phase as well as caveats of using the classical Monte Carlo method.