  Galaxies exhibit different clustering and quenching properties in clusters,
filaments, and the field, but it is still uncertain whether such differences
are imprints of the tidal environment on galaxy formation, or if they reflect
the variation of the underlying halo mass function across the cosmic web. We
measure the dependence of galaxy clustering and quenching on the cosmic web in
the Sloan Digital Sky Survey, characterized by the combination of spherical
overdensity $\delta_8$ and tidal anisotropy $\alpha_5$ centred on each galaxy.
We find that galaxy clustering is a strong function of either $\delta_8$ or
$\alpha_5$, and the large-scale galaxy bias shows complex and rich behaviour on
the $\delta_8$ vs. $\alpha_5$ plane. Using the mean galaxy colour as a proxy
for the average quenched level of galaxies, we find that galaxy quenching is
primarily a function of $\delta_8$, with some subtle yet non-trivial dependence
on $\alpha_5$ at fixed $\delta_8$. The quenched galaxies generally show
stronger small-scale clustering than the star-forming ones at fixed $\delta_8$
or $\alpha_5$, while the characteristic scale at which the amplitude of
clustering becomes comparable for both galaxy populations varies with
$\delta_8$ and $\alpha_5$. We compare these observed cosmic web dependences of
galaxy clustering and quenching with a mock galaxy catalogue constructed from
the iHOD model, which places quenched and star-forming galaxies inside dark
matter haloes based on the stellar-to-halo mass relation and the halo quenching
model --- the $\delta_8$ and $\alpha_5$ dependences of iHOD galaxies are thus
solely derived from the cosmic web modulation of the halo mass function. The
main observed trends are accounted for extremely well by the iHOD model. Thus
any additional direct effect of the large-scale~(${>}5\,h^{-1}{\rm Mpc}$) tidal
field on galaxy formation must be extremely weak. [Abridged]
