Recent advances in portable imaging have made camera-based screen capture ubiquitous. Unfortunately, frequency aliasing between the camera's color filter array (CFA) and the display's sub-pixels induces moir\'e patterns that severely degrade captured photos and videos. Although various demoir\'eing models have been proposed to remove such moir\'e patterns, these approaches still suffer from several limitations: (i) spatially varying artifact strength within a frame, (ii) large-scale and globally spreading structures, (iii) channel-dependent statistics and (iv) rapid temporal fluctuations across frames. We address these issues with the Moir\'e Conditioned Hybrid Adaptive Transformer (MoCHA-former), which comprises two key components: Decoupled Moir\'e Adaptive Demoir\'eing (DMAD) and Spatio-Temporal Adaptive Demoir\'eing (STAD). DMAD separates moir\'e and content via a Moir\'e Decoupling Block (MDB) and a Detail Decoupling Block (DDB), then produces moir\'e-adaptive features using a Moir\'e Conditioning Block (MCB) for targeted restoration. STAD introduces a Spatial Fusion Block (SFB) with window attention to capture large-scale structures, and a Feature Channel Attention (FCA) to model channel dependence in RAW frames. To ensure temporal consistency, MoCHA-former performs implicit frame alignment without any explicit alignment module. We analyze moir\'e characteristics through qualitative and quantitative studies, and evaluate on two video datasets covering RAW and sRGB domains. MoCHA-former consistently surpasses prior methods across PSNR, SSIM, and LPIPS.