Stress Granules (SG) formation is a cellular protection mechanism in harmful conditions, constituting a storage for untranslated mRNAs and RNA-binding proteins (RBPs); however, these condensates can turn into pathological aggregates, that in neurons are related to the onset of neurodegenerative diseases, like Amyotrophic Lateral Sclerosis (ALS). Mutations in the RBP FUS leading to its cytoplasmic mis-localization are causatively linked to ALS, since they mediate its accumulation in SGs, triggering their transition towards cytotoxic inclusions. Here, we describe the SG transcriptome in a neural context and compare with datasets from other systems, identifying both common rules and diversifying characteristics for SG recruitment of transcripts. We demonstrate that SG dynamics and RNA content are strongly modified by the incorporation of aberrantly localized mutant FUS, switching to a more unstructured, AU-rich SG transcriptome and losing a wide population of GC-rich, structured RNAs. We show that these alterations mainly depend on mutant FUS which favors the SG incorporation of its protein interactors and in turn of their target RNAs. Our data give a comprehensive view of the molecular differences between physiological and pathological SG in ALS conditions, showing how a single mutation is sufficient to impact the RNA and protein population of these condensates.