The judiciary can be caught in the middle when procedures have been affected by alterations in the balance of powers. But they should know better than to create work-arounds. These will always make bigger problems in the long run.
The public can always file lawsuits, but that doesn’t satisfy the Grievance clause. Not everything is a matter for the courts. Political questions, for one - although politics has found the judiciary with many more elections and campaigning, and we need to address the ever-expanding definition of a political question.
And both state and federal judges are officers of the United States and must uphold federal law above any state law or constitution contradicting it (see Restoring the Preamble, Restoring Invalidly Amended Text, and The Rule of Law).
"This Constitution, and the Laws of the United States
which shall be made in Pursuance thereof; and all Treaties made,
or which shall be made, under the Authority of the United States,
shall be the supreme Law of the Land; and the Judges of every State
shall be bound thereby, any Thing in the Constitution or Laws of
any State to the Contrary notwithstanding."
Even when states are “labbing”, or experimenting with, a possible change (see The Public Grievance Question), they must rule in favor of the federal law the “lab” is looking at changing.
Every power is delegated for the purpose of performing a responsibility. Officers, especially elected officers who are accountable directly to the voters, try to make themselves more popular by encroaching on other officers' more popular powers and abdicating their own less popular powers (responsibilities). They also encroach and abdicate for overall power advantage, and sometimes for financial gain.
Discretion, privilege, immunity, deference and sovereignty are all ways that branches and levels of government try to encroach on one anothers' powers or abdicate their own. These five concepts, in various ways, place officers above the law or detach powers from the responsibilities that define them and limit their action.
Judges and Justices aren't immune to these desires, which can cause a problem when they have to adjudicate disputes between other government actors.
Sometimes state courts must defer questions to federal courts and vice versa. And sometimes the judiciary defers details of execution or enforcement to administrative courts. This must be done cautiously. Inappropriate judicial deference is abdication.