A key challenge in dual-polarized multiplexing for joint radar and communication (JRC) systems is cross-polarization (cross-pol) leakage caused by depolarization. In conventional MIMO systems, depolarization arises solely from the channel; however, in XL-MIMO systems, non-stationary properties of the array cause additional polarization shifts at each antenna element, further degrading JRC performance. This paper introduces a channel model incorporating polarization shifts due to the propagation channel and antenna elements in the near-field. We also propose an antenna selection (AS) scheme that dynamically chooses antennas based on polarization imbalance and cross-pol leakage, enhancing spectral efficiency, symbol error rate, and radar detection probability. Simulations show that the proposed AS significantly outperforms traditional methods, providing scalable benefits for XL-MIMO JRC systems.