We investigate polarization-insensitive waveguide designs afforded by the interplay of material and waveguide birefringence in LiNbO3-on-insulator photonic wires. Fundamental mode birefringence-free operation in the 0.8-1.8 μm spectral range is predicted for a suitable choice of waveguide widths in the 375-600 nm range. Optimized buried waveguide designs yield broadband (1350-1625 nm) index matching between TE00 and TM00 modes. Furthermore, simultaneous phase- and group-velocity matching at infrared wavelengths appears feasible for pulse durations as short as 100 fs.