With the emergence of diverse and massive data in the upcoming sixth-generation (6G) networks, the task-agnostic semantic communication system is regarded to provide robust intelligent services. In this paper, we propose a task-agnostic learnable weighted-knowledge base semantic communication (TALSC) framework for robust image transmission to address the real-world heterogeneous data bias in KB, including label flipping noise and class imbalance. The TALSC framework incorporates a sample confidence module (SCM) as meta-learner and the semantic coding networks as learners. The learners are updated based on the empirical knowledge provided by the learnable weighted-KB (LW-KB). Meanwhile, the meta-learner evaluates the significance of samples according to the task loss feedback, and adjusts the update strategy of learners to enhance the robustness in semantic recovery for unknown tasks. To strike a balance between SCM parameters and precision of significance evaluation, we design an SCM-grid extension (SCM-GE) approach by embedding the Kolmogorov-Arnold networks (KAN) within SCM, which leverages the concept of spline refinement in KAN and enables scalable SCM with customizable granularity without retraining. Simulations demonstrate that the TALSC framework effectively mitigates the effects of flipping noise and class imbalance in task-agnostic image semantic communication, achieving at least 12% higher semantic recovery accuracy (SRA) and multi-scale structural similarity (MS-SSIM) compared to state-of-the-art methods.