Public employee unions must be declared unconstitutional as a start. Then and only then can the swamp be dismantled.
On the federal level, yes. Generally, the Constitution is aimed at the feds, not the states. The Constitution is the only legitimate source of authority of the feds and it does not give the feds any power to enforce unions.
However, in our Free Constitutional Republic, the people of each state are generally the only legitimate source of power and authority for the states. The Constitution does not forbid states to enforce unions. That is up to the people of each state.
Freedom is only as good as those willing to fight for it and maintain it.