  We explore the redshift evolution of a curious correlation between the
star-formation properties of central galaxies and their satellites (`galactic
conformity') at intermediate to high redshift ($0.4<z<1.9$). Using an extremely
deep near-infrared survey, we study the distribution and properties of
satellite galaxies with stellar masses, ${\rm log} ({\rm M}_*/{\rm
M}_{\odot})>9.7$, around central galaxies at the characteristic Schechter
function mass, ${\rm M} \sim {\rm M}^{\ast}$. We fit the radial profiles of
satellite number densities with simple power laws, finding slopes in the range
-1.1 to -1.4 for mass-selected satellites, and -1.3 to -1.6 for passive
satellites. We confirm the tendency for passive satellites to be preferentially
located around passive central galaxies at $3\sigma$ significance and show that
it exists to at least $z\sim2$. Meanwhile, the quenched fraction of satellites
around star-forming galaxies is consistent with field galaxies of equal stellar
masses. We find no convincing evidence for a redshift-dependent evolution of
these trends. One simple interpretation of these results is that only passive
central galaxies occupy an environment that is capable of independently
shutting off star-formation in satellite galaxies. By examining the satellites
of higher stellar mass star-forming galaxies (${\rm log} ({\rm M}_*/{\rm
M}_{\odot}) > 11$), we conclude that the origin of galactic conformity is
unlikely to be exclusively due to the host dark-matter halo mass. A
halo-mass-independent correlation could be established by either formation bias
or a more physical connection between central and satellite star-formation
histories. For the latter, we argue that a star-formation (or AGN) related
outburst event from the central galaxy could establish a hot halo environment
which is then capable of quenching both central and satellite galaxies.
