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We study the effects of galaxy formation physics on the magnetization of the intergalactic medium (IGM) using the IllustrisTNG simulations. We demonstrate that large-scale regions affected by the outflows from galaxies and clusters contain magnetic fields that are several orders of magnitude stronger than in unaffected regions with the same electron density. Moreover, like magnetic fields amplified inside galaxies, these magnetic fields do not depend on the primordial seed, i.e. the adopted initial conditions for magnetic field strength. We study the volume filling fraction of these strong field regions and their occurrence in random lines of sight. As a first application, we use these results to put bounds on the photon-axion conversion from spectral distortion of the CMB. As photon-axion coupling grows with energy, stronger constraints could potentially be obtained using data on the propagation of gamma-ray photons through the IGM. Finally, we also briefly discuss potential applications of our results to the Faraday Rotation measurements.