Human-robot interaction (HRI) is an important component to improve the flexibility of modern production lines. However, in real-world applications, the task (\ie the conditions that the robot needs to operate on, such as the environmental lighting condition, the human subjects to interact with, and the hardware platforms) may vary and it remains challenging to optimally and efficiently configure and adapt the robotic system under these changing tasks. To address the challenge, this paper proposes a task-agnostic adaptable controller that can 1) adapt to different lighting conditions, 2) adapt to individual behaviors and ensure safety when interacting with different humans, and 3) enable easy transfer across robot platforms with different control interfaces. The proposed framework is tested on a human-robot handover task using the FANUC LR Mate 200id/7L robot and the Kinova Gen3 robot. Experiments show that the proposed task-agnostic controller can achieve consistent performance across different tasks.