The fundamental assumption of statistical mechanics is that, "In an isolated system in thermal equilibrium, all accessible microstates are equally probable (according to Schroeder)." So what goes wrong when equilibrium is not there in this statement? I could equally well imagine all the microstates to be equally probable in that case too. Also why the system has to be isolated?
"All states are equally probable" means in this context: "If I let the system relax for a long enough time, the system can be in each of its accessible microstates afterwards with the same probability."
Before the system has reached equilibrium, the probabilities of the individual microstates can obviously depend on how we prepared the system in the first place. (For example, directly after starting the experiment, the system has a very high probability to be in a microstate that is close to the original one.)
The same happens in the case where it never reaches equilibrium.
Also why the system has to be isolated?
Well, for example. If we turn on a magnetic field that forces the particle in one direction, that can influence those probabilities. We can include the magnetic field in the description, then the whole system is isolated and everything makes sense. But we can not just leave the magnetic field out of our description and still expect reasonable results.