Integrated sensing and communication (ISAC) systems often suffer severe performance degradation due to strong clutter echoes, and spatial-only beamforming is often inadequate for realistic array sizes. This paper addresses clutter suppression in ISAC by leveraging compound reconfigurable antenna (CRA) arrays, which simultaneously enable dynamic adjustment of both radiation patterns and polarization states, thus substantially expanding the degrees of freedom available in the electromagnetic (EM) domain. We develop a unified compound channel model that integrates virtual angular-domain responses, spatial propagation, and polarization rotation/depolarization. Leveraging statistical information about target and clutter covariances, we formulate a joint EM-domain and baseband-domain optimization aimed at maximizing the radar signal-to-clutter-plus-noise ratio (SCNR). The formulation also enforces multiuser downlink signal-to-interference-plus-noise ratio constraints, a total transmit-power budget, and finite-codebook EM-mode selection. The resulting nonconvex mixed-integer problem is tackled by an alternating algorithm that combines fractional programming and majorization-minimization with second-order cone programming-based updates and a penalty relaxation for mode selection. Extensive simulations in QuaDRiGa-based channel environments validate the effectiveness of the proposed CRA array design, demonstrating up to 11 dB SCNR improvements over conventional beamforming methods relying solely on baseband-domain optimization and confirming the substantial benefits of fully exploiting EM-domain reconfigurability for clutter-rich ISAC scenarios.