A very brief, although somewhat incomplete, answer would be that charge is related to a local symmetry, therefore with a gauge field that acts in the whole spacetime, even if the charges are inside the event horizon you could use the electromagnetic field to probe it. Lepton and Baryon number, or other flavour related quantities are related to global symmetries, and therefore once inside the horizon there is nothing that can physically probe this numbers.
The incompleteness of the answer is related to the other gauge fields, namely the carriers of weak and strong forces. Note that by no-hair conjecture the black hole should not contain this charges either. As I think this is somewhat more complicated I'll just say that Einstein equations coupled with (classical) Yang-Mills fields allow for black hole solutions which violate no-hair conjecture, although this solutions are unstable and therefore if they are a valid counterexample is up to dispute. Scalar fields may also cause hairs to grow (sorry for the pun)
There is a Living Review in Relativity by Chrusciel, Costa and Heusler that addresses the black hole uniqueness theorem. Maybe the introduction will give you an idea of what part is theorem, what is false and what remains conjecture.
Also in the seventies there were some papers giving detailed calculations which suggest that lepton and baryon numbers are ill-defined for black holes and that they are not able to carry weak and strong charges. A typical example would be Bekenstein's "Transcendence of the Law of Baryon-Number Conservation in Black-Hole Physics" and references therein, specially by Hartle and Teitelboim.