  One of the most prominent challenges to the standard Lambda cold dark matter
($\Lambda$CDM) cosmology is the tension between the structure growth parameter
$S_8$ constrained by the cosmic microwave background (CMB) data and the smaller
one suggested by the cosmic shear data. Recent studies show that, for
$\Lambda$CDM cosmology, redshift-space distortion (RSD) data also prefers a
smaller $S_8$ that is $\sim 2$-$3\sigma$ lower than the CMB value, but the
result is sensitive to the cosmological model. In the present work we update
the RSD constraint on $S_8$ with the most up-to-date RSD data set where the
correlation between data points are properly taken into account. To reduce the
model dependence, we add in our Monte Carlo Markov Chain calculation the most
up-to-date data sets of Type Ia supernovae (SN) and baryon acoustic
oscillations (BAO), whose correlation with RSD is also taken into account, to
constrain the background geometry. For $\Lambda$CDM cosmology we find $S_8=
0.812 \pm 0.026$, which is $\sim 2\sigma$ larger than previous studies, and
hence is consistent with the CMB constraint. By replacing $\Lambda$CDM with the
Parameterization based on cosmic Age (PAge), an almost model-independent
description of the late universe, we find that the RSD + SN + BAO constraint on
$S_8$ is insensitive to the cosmological model.
