Thyroid ultrasound (US) automation couples two competing requirements: global, geometry-driven reasoning for nodule delineation and local, texture-driven reasoning for malignancy risk assessment. Under cross-center domain shift, these cues degrade asymmetrically, yet most multi-task pipelines rely on a single shared backbone, often inducing negative transfer. In this paper, we characterize this interference across CNN (ResNet34) and medical ViT (MedSAM) backbones, and observe a consistent trend: ViTs transfer geometric priors that benefit segmentation, whereas CNNs more reliably preserve texture cues for malignancy discrimination under strong shift and artifacts. Motivated by this failure mode, we propose a lightweight family of decoder-side adapters, the Multi-Kernel Gated Adapter (MKGA) and a residual variant (ResMKGA), which refine multi-scale skip features using complementary receptive fields and apply semantic, context-conditioned gating to suppress artifact-prone content before fusion. Across two US benchmarks, the proposed adapters improve cross-center robustness: they strengthen out-of-domain segmentation and, in the CNN setting, yield clear gains in clinical TI-RADS diagnostic accuracy compared to standard multi-task baselines. Code and models will be released.