  We study the high-temperature phase diagram of the chiral magnetic insulator
Cu$_2$OSeO$_3$ by measuring the spin-Hall magnetoresistance (SMR) in a thin Pt
electrode. We find distinct changes in the phase and amplitude of the SMR
signal at critical lines separating different magnetic phases of bulk
Cu$_2$OSeO$_3$. The skyrmion lattice state appears as a strong dip in the SMR
phase. A strong enhancement of the SMR amplitude is observed in the conical
spiral state, which we explain by an additional symmetry-allowed contribution
to the SMR present in non-collinear magnets. We demonstrate that the SMR can be
used as an all-electrical probe of chiral surface twists and skyrmions in
magnetic insulators.
