  Constraining quantum gravity from observations is a challenge. We expand on
the idea that the interplay of quantum gravity with matter could be key to
meeting this challenge. Thus, we set out to confront different potential
candidates for quantum gravity -- unimodular asymptotic safety, Weyl-squared
gravity and asymptotically safe gravity -- with constraints arising from
demanding an ultraviolet complete Standard Model. Specifically, we show that
within approximations, demanding that quantum gravity solves the Landau-pole
problems in Abelian gauge couplings and Yukawa couplings strongly constrains
the viable gravitational parameter space. In the case of Weyl-squared gravity
with a dimensionless gravitational coupling, we also investigate whether the
gravitational contribution to beta functions in the matter sector calculated
from functional Renormalization Group techniques is universal, by studying the
dependence on the regulator, metric field parameterization and choice of gauge.
