  We report investigations of the structural, magnetic, electrical transport
and thermal properties of five compositions of the metallic perovskite
GdRh$_3$C$_{1-x}$B$_x$ ($0.00 \le x \le 1.00$). Our results show that all the
five compositions undergo magnetic ordering at low temperatures, but the nature
of the ordered state is significantly different in the carbon- and the
boron-rich compositions, where the former shows signatures of an
amplitude-modulated magnetic structure and the latter exhibits evidences of an
equal-moment incommensurate antiferromagnetic ordering. We also observe a
remarkable field-dependent evolution of conduction carrier polarization in the
compositionally disordered compounds. The outcomes indicate that this system is
energetically situated in proximity to a magnetic instability where small
variations in the control parameter(s), such as lattice constant and/or
electron density, lead to considerably different ground states.
