Can stellar black holes cancel each other? Hypothetical question: when a pair of identical stellar black holes are very close to one another wouldn't the side facing each other experience lower gravitational force? How is this logic un/sound?
Your logic isn't unsound. By symmetry there would be a gravitational neutral point between them.

Of course, the black holes could not then be described by the Schwarzschild metric, since that only applies to a spherically symmetric situation.

As you brought the black holes closer together, the isopotentials would become distinctly aspherical, the event horizons would be complicated shapes and ultimately would merge - although as the black holes would presumably be in orbit and rotating, the spacetime geometry would be even more complex than that.