Antiferromagnetic conductors with suitably broken spatial symmetries host spin-polarized bands, which lead to transport phenomena commonly observed in metallic ferromagnets. In bulk materials, it is the given crystalline structure that determines whether symmetries are broken and spin-polarized bands are present. Here we show that, in the two-dimensional limit, an electric field can control the relevant symmetries. To this end, we fabricate a double-gate transistor based on bilayers of van der Waals antiferromagnetic semiconductor CrPS₄ and show how a perpendicular electric displacement field can switch the spin polarization of the conduction band on and off. Because conduction band states with opposite spin polarizations are hosted in the different layers and are spatially separated, these devices also give control over the magnetization of the electrons that are accumulated electrostatically. Our experiments show that double-gated CrPS₄ transistors provide a viable platform to create gate-induced conductors with near unity spin polarization at the Fermi level, as well as devices with a full electrostatic control of the total magnetization of the system.