Intracellular aggregation of repeat expanded RNA has been implicated in many neurological disorders. Here, we study the role of biomolecular condensates on irreversible RNA clustering. We find that physiologically relevant, and disease-associated repeat RNAs spontaneously undergo an age-dependent percolation transition inside multi-component protein-nucleic acid condensates to form nanoscale clusters. Homotypic RNA clusters drive the emergence of multiphasic condensate structures, with an RNA-rich solid core surrounded by an RNA-depleted fluid shell. The timescale of the RNA clustering, which accompanies a liquid-to-solid transition of biomolecular condensates, is determined by the sequence features, stability of RNA secondary structure, and repeat length. Importantly, G3BP1, the core scaffold of stress granules, introduces heterotypic buffering to homotypic RNA-RNA interactions and impedes intra-condensate RNA clustering in an ATP-independent manner. Our work suggests that biomolecular condensates can act as sites for RNA aggregation. It also highlights the functional role of RNA-binding proteins in suppressing aberrant RNA phase transitions.