Why is the resting membrane potential of excitable tissue not affected by the extracellular sodium concentration?
I cannot imagine anyone being able to explain it more clearly than this webpage. Your question is addressed in the middle of the page.

It's easier to split the idea into two separate, but parallel ideas: electrical potential and chemical potential. Both sodium and potassium contribute to resting potential. Sodium affects the voltage (electric potential) across the membrane. However, their chemical potentials (difference-across-membrane) are separate. The key idea is that there is a difference between resting membrane potential and potassium equilibrium potential. 

I quote a helpful thing to keep in mind:

In a neuron, the resting membrane potential is closer to the potassium equilibrium potential than it is to the sodium equilibrium potential. That's because the resting membrane is much more permeable to K+ than to Na+.

    If more potassium channels were to open up—making it even easier for K+ to cross the cell membrane—the membrane would hyperpolarize, getting even closer to the potassium equilibrium potential.
    If, on the other hand, additional sodium channels were to open up—making it easier for Na+ to cross the membrane—the cell membrane would depolarize toward the sodium equilibrium potential.