The issue is visible in Fig. 1.
The dashed curves show the parallax distribution expected if MW Cepheids followed a single uniform-in-volume (spherical) prior without selection.
But the observed Cepheids (two samples, red and green, with different selection functions) clearly don’t look like that, they live in the Galactic disk and are shaped by survey selection (closer, less extinction).
If the prior selection don’t reproduce the observed distributions, the inference gets biased.