Computational RNA design has broad applications across synthetic biology and therapeutic development. Fundamental to the diverse biological functions of RNA is its conformational flexibility, enabling single sequences to adopt a variety of distinct 3D states. Currently, computational biomolecule design tasks are often posed as inverse problems, where sequences are designed based on adopting a single desired structural conformation. In this work, we propose gRNAde, a geometric RNA design pipeline that operates on sets of 3D RNA backbone structures to explicitly account for and reflect RNA conformational diversity in its designs. We demonstrate the utility of gRNAde for improving native sequence recovery over single-state approaches on a new large-scale 3D RNA design dataset, especially for multi-state and structurally diverse RNAs. Our code is available at https://github.com/chaitjo/geometric-rna-design