Let's say a black hole of mass $M$ and a very compact lump of anti-matter (not a singularity) also of mass $M$ are traveling toward each other. What does an outside observer see when they meet?
Will they blow themselves apart in a matter/anti-matter reaction? Or will their masses combine, never quite meeting in the infinite time dilation at the event horizon?
Answer
Whether the infalling material is matter or antimatter makes no difference.
Fundamentally, the confusion probably comes from thinking of black holes as normal substances (and thus retaining the properties of whatever matter went into making them). Really, a black hole is a region of spacetime with certain properties, notably the one-way surface we call an event horizon. That's it. Whatever you envision happening on the inside of a black hole, whether it be a singularity or angels dancing on the head of a pin, is completely irrelevant.
The reason spacetime is curved enough to form an event horizon is essentially the due to the density of mass and energy in the area. Antimatter counts just the same as matter when it comes to mass and energy. Anti-protons have the same, positive mass as normal protons, and at a given speed they have the same, positive kinetic energy too.
Even if you wanted matter and antimatter to annihilate somewhere near/inside a black hole, the resulting photons would cause no less curvature of spacetime, as all particle physics reactions conserve energy and momentum. This is related to how you could form a black hole from nothing but radiation.
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