Finiteness conjecture for regional fundamental groups of dlt rationally connected pairs

Let $X$ be a rationally connected variety, and let $(X,\Delta)$ be a dlt pair. Write $\pi_1^{\rm reg}(X)$ for the regional fundamental group. Finiteness conjecture for regional fundamental groups. The group $\pi_1^{\rm reg}(X)$ is finite.

The conjecture is motivated by the contrast between Fano type and singular rationally connected varieties: rationally connected varieties can have infinite regional fundamental group in the singular setting, but the source expects finiteness for dlt pairs. It remains open.