We study the influence of spinless impurities on a frustrated magnet featuring a spin-density wave (stripe) phase by means of Monte Carlo simulations. We demonstrate that the interplay between the impurities and an order parameter that breaks a real-space symmetry triggers the emergence of a random-field mechanism which destroys the stripe-ordered phase. Importantly, the strength of the emerging random fields can be tuned by the repulsion between the impurity atoms; they vanish for perfect anticorrelations between neighboring impurities. This provides a way of controlling the phase diagram of a many-particle system. In addition, we also investigate the effects of the impurities on the character of the phase transitions between the stripe-ordered, ferromagnetic, and paramagnetic phases. © 2018 American Physical Society.