  We show that the Brauer-Manin obstruction is the only obstruction to strong
approximation for all stacky curves over global fields with finite abelian
fundamental groups. This includes all stacky curves of genus $g = \frac{1}{2}$,
thus explaining a recent counterexample to the Hasse principle of
Bhargava-Poonen. We will furthermore show that the elementary obstruction is
the only obstruction to the integral Hasse principle for smooth proper integral
models of stacky curves of genus $g < 1$. We then compute the Brauer-Manin
obstruction for smooth proper integral models of stacky curves of genus
$\frac{1}{2}$.
