  We prove that a strongly $F$-regular scheme $X$ admits a finite, generically
Galois, and \'etale-in-codimension-one cover $\widetilde X \to X$ such that the
\'etale fundamental groups of $\widetilde X$ and $\widetilde X_{reg}$ agree.
Equivalently, every finite \'etale cover of $\widetilde X_{reg}$ extends to a
finite \'etale cover of $\widetilde X$. This is analogous to a result for
complex klt varieties by Greb, Kebekus and Peternell.
