Does existence of isotropic background radiation contradict relativity?

Answer 1

No, it would be consistent with general relativity's big bang solution to the origin of the universe, per se. However, it would present other problems such as how the galaxies formed without any significant density perturbations at the time the background radiation was emitted. Fortunately, as the first responder notes, that is not the case. That actual perturbations seen are consistent with galaxy formation.

Answer 2

Actually, the COBE observations showed it to be slightly anistropic.