This is true in boolean categories (extensive + terminal object + (T : 1 → 1 + 1) is subobject classifier), but for any monic, not just split monics. There's quite a nice and easy read on extensive categories from 93:
Carboni et al. Introduction to extensive and distributive categories. Journal of Pure and Applied Algebra (1993) vol. 84 pp. 145-158
However, modulo axiom of choice, all monics in Set split, and I suspect this could be true for any boolean category.
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