Large Language Models, the dominant starting point for Natural Language Processing (NLP) applications, fail at a higher rate for speakers of English dialects other than Standard American English (SAE). Prior work addresses this using task specific data or synthetic data augmentation, both of which require intervention for each dialect and task pair. This poses a scalability issue that prevents the broad adoption of robust dialectal English NLP. We introduce a simple yet effective method for task-agnostic dialect adaptation by aligning non-SAE dialects using adapters and composing them with task-specific adapters from SAE. Task-Agnostic Dialect Adapters (TADA) improve dialectal robustness on 4 dialectal variants of the GLUE benchmark without task-specific supervision.