Recent works have demonstrated that attention-based transformer and large language model (LLM) architectures can achieve strong channel state prediction (CSP) performance by capturing long-range temporal dependencies across channel state information (CSI) sequences. However, these models suffer from quadratic scaling in sequence length, leading to substantial computational cost, memory consumption, and inference latency, which limits their applicability in real-time and resource-constrained wireless deployments. In this paper, we investigate whether selective state space models (SSMs) can serve as a hardware-efficient alternative for CSI prediction. We propose MambaCSP, a hybrid-attention SSM architecture that replaces LLM-based prediction backbones with a linear-time Mamba model. To overcome the local-only dependencies of pure SSMs, we introduce lightweight patch-mixer attention layers that periodically inject cross-token attentions, helping with long-context CSI prediction. Extensive MISO-OFDM simulations show that MambaCSP improves prediction accuracy over LLM-based approaches by 9-12%, while delivering up to 3.0x higher throughput, 2.6x lower VRAM usage, and 2.9x faster inference. Our results demonstrate that hybrid state space architectures provide a promising direction for scalable and hardware-efficient AI-native CSI prediction in future wireless networks.