We present three-dimensional moving-mesh hydrodynamical simulations () of equal-mass binaries in circumbinary discs, spanning binary eccentricity (e = 0.0, 0.3, 0.6) and inclination (i = 0^∘--60^∘), using a locally isothermal α-disc (H/r = α_(rm visc) = 0.1) with fixed Keplerian orbits. Discs above the critical inclination i_(rm crit)(e), decreasing with e, drive their interiors near-polar, so eccentricity alone alters the outcome at fixed i. Discs reach polar alignment ten times faster than they align toward the binary plane, settling long before the binary's orbit responds. Alignment dictates how the disc acts on the binary. First, a disc tilting back toward the binary plane spends nearly all its torque reorienting the binary's orbit, whereas a disc driven polar redirects it into the orbit itself, which shrinks 10–20 times faster. Second, at e = 0.6 the turn to polar is a single transient reshaping the accretion flow, cavity and orbit, with accretion enhanced (i = 45^∘) or suppressed (i = 60^∘). Third, misalignment suppresses coplanar eccentricity pumping: the attractor at e ≈ 0.4 survives only below i ≈ 15^∘, so misaligned binaries circularise and may enter the gravitational-wave regime less eccentric than coplanar models predict. Around a circular binary, the familiar ≈ 4.5-orbit accretion modulation vanishes while the disc is strongly warped, returning as it realigns, a time-domain signature of misaligned massive black-hole binaries. Finally, observed polar discs around stellar binaries, such as HD 98800 BaBb's, are likely in their final state; intermediate misalignments reflect slower alignment toward the binary plane.