Linearly Polarized (LP) modes are popular for fiber-optic communication systems, yet on-chip LP mode manipulation remains challenging. We propose a method for chiral switching of LP modes by avoiding exceptional points in non-Hermitian systems. By adjusting one waveguide's radius and trajectory in a dual-coupled system, chiral LP mode switching is achieved, with output direction determined by the path. More importantly, the proposed chip can simultaneously support two polarization states, which is highly significant for compatibility with polarization division multiplexing systems. This work offers a new approach for on-chip LP mode control.