Certainly, an isolated system at equilibrium will remain so when isolated. This example is a bit of a tautology though. But the implications are important, because we next have to consider non-isolated systems.
An open system allows mass flow but may have an insulated boundary. A closed system allows no mass flow but may have a diathermal boundary. Finally, a system may allow mass and heat flow (as well as flow of other work).
While these systems can be in steady state, can they be in true equilibrium? See the discussion here. The answer is no. They can be at steady state, a quasi-equilibrium condition.
The instant a non-isolated system under steady state conditions is isolated, its steady state is lost. The once non-isolated system that is now isolated can then move to its true equilibrium.
But, though a non-isolated system that is suddenly isolated can move its state, will it move its state? Think about a refrigerator that is losing heat and being cooled to make up. Allow a bit of air flow leaking in and out at various places around the doorway. The inside is at a steady state temperature and pressure (and chemical potential and ...). Now, isolate that system. No heat or mass flow is allowed at all. The result is, the inside of the refrigerator will remain at the temperature (and pressure and chemical potential) that it had at the instant it is isolated. Why would it change?
OK, we have taken out chemical reactions from this consideration (oh no, we forgot that we left both yogurt and mold spores inside). When a chemical reaction is occurring in a steady state (non-isolated) system, it may not be at its true chemical equilibrium within the confines of the system. We only need to realize that we purge mold spores (and yogurt) in/out of the refrigerator over a steady period to see the difference. Once the system is isolated, the mold can grow freely to a new equilibrium state.
So, systems that are not isolated to start and are at steady state but include chemical reactions may not remain at the state they have when they are instantly isolated. They can change internally because the chemical reaction itself was only at a quasi-equilibrium state, not a true (isolated case) equilibrium state.
What about non-isolated systems that act as isolated systems because they have no flows across their boundaries. If they are at equilibrium, they remain so when isolated.
In summary, the connection that is to be made is that equilibrium is a state only of isolated systems or systems that behave exactly as such to start. The question itself is therefore somewhat a tautological one.