No, it does not. A post-truth era may be one in which truth & falsity are not absolute & the only choices. Relativity brings about the realization that two people can witness the same event, obtain different measurements (usual example is in "empty" space where both start at the same velocity & distance to the event location, but one is in an accelerating reference frame relative to the other leading to different photon counts & "time" passage) & both be correct.