Single-cell RNA sequencing (scRNA-seq) analyses typically focus on alignment and differential gene expression, being blind to other transcriptome variation. Here we present sc-SPLASH for statistics-first, reference-free discovery on barcoded scRNA-seq and spatial transcriptomics; its independent BKC submodule optimizes barcoded data preprocessing and is approximately 50-fold faster than UMI-tools. sc-SPLASH discovers secreted repeat proteins in immune-like cells of sponge (Spongilla; missing from the reference) and tunicate (Ciona). sc-SPLASH extends reference-free analysis to barcoded single-cell and spatial transcriptomics data.