Physical caregiving robots hold promise for improving the quality of life of millions worldwide who require assistance with feeding. However, in-home meal assistance remains challenging due to the diversity of activities (e.g., eating, drinking, mouth wiping), contexts (e.g., socializing, watching TV), food items, and user preferences that arise during deployment. In this work, we propose FEAST, a flexible mealtime-assistance system that can be personalized in-the-wild to meet the unique needs of individual care recipients. Developed in collaboration with two community researchers and informed by a formative study with a diverse group of care recipients, our system is guided by three key tenets for in-the-wild personalization: adaptability, transparency, and safety. FEAST embodies these principles through: (i) modular hardware that enables switching between assisted feeding, drinking, and mouth-wiping, (ii) diverse interaction methods, including a web interface, head gestures, and physical buttons, to accommodate diverse functional abilities and preferences, and (iii) parameterized behavior trees that can be safely and transparently adapted using a large language model. We evaluate our system based on the personalization requirements identified in our formative study, demonstrating that FEAST offers a wide range of transparent and safe adaptations and outperforms a state-of-the-art baseline limited to fixed customizations. To demonstrate real-world applicability, we conduct an in-home user study with two care recipients (who are community researchers), feeding them three meals each across three diverse scenarios. We further assess FEAST's ecological validity by evaluating with an Occupational Therapist previously unfamiliar with the system. In all cases, users successfully personalize FEAST to meet their individual needs and preferences. Website: https://emprise.cs.cornell.edu/feast