Establishing trustworthiness is fundamental for the responsible utilization of medical artificial intelligence (AI), particularly in cancer diagnostics, where misdiagnosis can lead to devastating consequences. However, there is currently a lack of systematic approaches to resolve the reliability challenges stemming from the model limitations and the unpredictable variability in the application domain. In this work, we address trustworthiness from two complementary aspects—data trustworthiness and model trustworthiness—in the task of subtyping non-small cell lung cancers using whole side images. We introduce TRUECAM, a framework that provides trustworthiness-focused, uncertainty-aware, end-to-end cancer diagnosis with model-agnostic capabilities by leveraging spectral-normalized neural Gaussian Process (SNGP) and conformal prediction (CP) to simultaneously ensure data and model trustworthiness. Specifically, SNGP enables the identification of inputs beyond the scope of trained models, while CP offers a statistical validity guarantee for models to contain correct classification. Systematic experiments performed on both internal and external cancer cohorts, utilizing a widely adopted specialized model and two foundation models, indicate that TRUECAM achieves significant improvements in classification accuracy, robustness, fairness, and data efficiency (i.e., selectively identifying and utilizing only informative tiles for classification). These highlight TRUECAM as a general wrapper framework around medical AI of different sizes, architectures, purposes, and complexities to enable their responsible use.