Affine Schubert varieties are a generalization of classical Schubert varieties arising in the study of the local structure of Shimura varieties. Faltings and Pappas-Rapoport generalized the classical work of Mehta-Ramanathan to the affine case, and in particular, they showed that these varieties are Frobenius split. In this talk I discuss a different approach to constructing Frobenius splittings, as well as splittings for more general finite covers, leading to new perspectives on F-regularity. This is joint work in progress with J. Lourenço.