Why can objects observed very far away appear to recede at speeds greater than $c$ without violating relativity?

It is the space between the observer and the distant galaxy that is expanding rapidly, causing apparent recession velocity to exceed $c$.

The apparent recession of objects faster than the speed of light ($c$) is a non-intuitive but permitted consequence of General Relativity applied to the dynamic universe. Einstein's theory strictly forbids any object or information from moving *through* space faster than $c$. However, the expansion of the universe involves the metric expansion of spacetime itself. For extremely distant galaxies, the space separating us is expanding so rapidly that the aggregate recession velocity, which is the sum of the galaxy's velocity through its local space plus the expansion of the intervening space, exceeds $c$. Since this is space stretching, not movement *through* space, relativity remains intact.