Recent work suggests that asymmetric segregation of preexisting and newly synthesized canonical histone 3.1 (H3.1), but not variant histone 3.3A (H3.3A), plays an important role in the asymmetric outcome of Drosophila germline stem cell (GSC) and intestinal stem cell (ISC) divisions. However, this finding relied on the Gal4/UAS system and Flp-out technology to swap expression of exogenous fluorescent proteins—an approach that decouples H3.1 expression from the cell cycle and may be prone to artifacts. Here, by photoswitching photoconvertible H3-Dendra2 proteins expressed under their native controls in living flies, we find that preexisting and newly synthesized H3.1 and H3.3A are symmetrically segregated in dividing ISCs and somatic cyst stem cells (CySCs) in male testes. While H3.3A was found to be symmetrically segregated during GSC divisions, analysis of the H3.1 segregation in GSCs was complicated by our unexpected finding that H3.1-Dendra2 expressed under its normal control within the context of a histone transgene is not detectable in GSCs, owing to regulatory elements in the 3’UTR that mediate translational repression by the RNA-binding proteins Nanos and Pumilio. Nevertheless, when this repression is obviated by using a 3’UTR devoid of such elements, H3.1-Dendra2 is expressed in GSCs and symmetrically segregated without affecting lineage outcomes. We obtained similar results when the coding sequence of H3.3A was edited to encode H3.1 in the context of an H3.3A-Dendra2 knock-in allele. Our findings thus challenge the prevailing model of asymmetric histone segregation and reveal an unexpected molecular mechanism of posttranscriptional repression of H3.1 in GSCs.