Across science and engineering, experimental and simulation-based studies increasingly rely on high-dimensional data to investigate complex physical systems. While data volumes have grown, resulting discoveries are often difficult to reproduce, compare, or transfer across settings. A central reason is that many data-driven workflows do not explicitly account for symmetry, i.e., transformations under which a system exhibits the same underlying behavior. As a result, physically equivalent experiments are treated as unrelated observations, leading to redundant parameters and fragile models. Dimensionless learning provides a practical entry point for symmetry-aware discovery. It can be interpreted as discovering scaling symmetry in parameter space, or equivalently translational symmetry in log-parameter space, allowing invariant structure to be identified directly from data. While effective, existing implementations of dimensionless learning and related symmetry-based methods remain fragmented and lack shared workflows for validation and reuse. In this work, we present OpenSymmetry, an open-source ecosystem that generalizes dimensionless learning within a broader framework for data-driven symmetry discovery. OpenSymmetry provides a canonical workflow, shared benchmarks, and standardized interfaces to support reproducible discovery of symmetry, scaling laws, and governing structures across domains. By treating symmetry discovery as shared scientific infrastructure, OpenSymmetry enables more interpretable, transferable, and robust data-driven modeling of complex physical systems.