  We provide uniform RR Lyrae-based distances to 39 dwarf galaxies in and
around the Local Group. We determine distances based on a Bayesian hierarchical
model that uses periods and magnitudes of published RR Lyrae in dwarf galaxies
and is anchored to well-studied Milky Way (MW) RR Lyrae with spectroscopic
metallicities and Gaia eDR3 parallaxes. Gaia eDR3 parallaxes for the anchor
sample are a factor of 2, on average, more precise than DR2 parallaxes, and
allow for a much better constrained period-luminosity-metallicity relation.
While $\sim75$% of our distances are within 1-$\sigma$ of recent literature RR
Lyrae distances, our distances are also $\sim2$-$3$ times more precise than
literature distances, on average. On average, our distances are $\sim0.05$ mag
closer than literature distances, as well as $\sim0.06$ mag closer than
distances derived using a theoretical period-luminosity-metallicity relation.
These discrepancies are largely due to our eDR3 parallax anchor. We show that
the Hipparcos-anchored RR Lyrae distance scale of Carretta et al. (2000)
over-predicts distances to MW RR Lyrae by $\sim0.05$ mag. The largest
uncertainties in our distances are (i) the lack of direct metallicity
measurements for RR Lyrae and (ii) the heterogeneity of published RR Lyrae
photometry. We provide simple formulae to place new dwarf galaxies with RR
Lyrae on a common distance scale with this work. We provide public code that
can easily incorporate additional galaxies and data from future surveys,
providing a versatile framework for cartography of the local Universe with RR
Lyrae.
