As far as I understand, when a federal court declares a federal statute unconstitutional, lower court simply adopts the same practice in the future and no repeal of the statute is required. But what if a state statute is declared unconstitutional in a federal court? Should state courts follow the precedent by the federal court?
Regardless of jurisdiction within the US, the courts have no power to compel repeal of a statute, which is a political process. (An overturned statute might be edited out of the code books, but actual repeal has to be done by the legislature). So it is never required to repeal a statute.
A statute becomes a legal nullity within the jurisdiction of the ruling court. State courts bind state courts, and federal courts bind federal courts. However, a SCOTUS ruling puts an end to any further discussion. Until SCOTUS speaks on a state issue, there is still room for disagreement. If a federal district court rules a city or state law unconstitutional, state courts do not have to obey that ruling. Even if a federal circuit court and a lower state court so rule, it is has to go to a court of final appeal. Once the state Supreme Court or US Supreme Court agrees, the question is resolved.