  We point out that in models of macroscopic topological defects composed of
one or more scalar fields that interact with standard-model fields via
scalar-type couplings, the back-action of ambient matter on the scalar field(s)
produces an environmental dependence of the fundamental constants of nature, as
well as spatial variations of the fundamental constants in the vicinity of
dense bodies such as Earth due to the formation of a "bubble-like" defect
structure surrounding the dense body. In sufficiently dense environments,
spontaneous symmetry breaking may be inhibited altogether for $\phi^2$
interactions, potentially delaying the cosmological production of topological
defects. We derive bounds on non-transient variations of the fundamental
constants from torsion-pendulum experiments that search for
equivalence-principle-violating forces, experiments comparing the frequencies
of ground- and space-based atomic clocks, as well as ground-based clocks at
different heights in the recent Tokyo Skytree experiment, and measurements
comparing atomic and molecular transition frequencies in terrestrial and
low-density astrophysical environments. Our results constrain the present-day
mass-energy fraction of the Universe due to a network of infinite domain walls
produced shortly after the BBN or CMB epochs to be $\Omega_{\textrm{walls},0}
\ll 10^{-10}$ for the symmetron model with a $\phi^4$ potential and $\phi^2$
interactions, improving over CMB quadrupolar temperature anisotropy bounds by
at least 5 orders of magnitude. Our newly derived bounds on domain walls with
$\phi^2$ interactions via their effects of non-transient variations of the
fundamental constants are significantly more stringent than previously reported
clock- and cavity-based limits on passing domain walls via transient signatures
and previous bounds from different types of non-transient signatures, under the
same set of assumptions.
