As atmospheric CO₂ concentrations rise, associated ocean warming (OW) and ocean acidification (OA) are predicted to cause declines in reef‐building corals globally, shifting reefs from coral‐dominated systems to those dominated by less sensitive species. Sponges are important structural and functional components of coral reef ecosystems, but despite increasing field‐based evidence that sponges may be ‘winners’ in response to environmental degradation, our understanding of how they respond to the combined effects of OW and OA is limited. To determine the tolerance of adult sponges to climate change, four abundant Great Barrier Reef species were experimentally exposed to OW and OA levels predicted for 2100, under two CO₂ Representative Concentration Pathways (RCPs). The impact of OW and OA on early life‐history stages was also assessed for one of these species to provide a more holistic view of species impacts. All species were generally unaffected by conditions predicted under RCP6.0, although environmental conditions projected under RCP8.5 caused significant adverse effects: with elevated temperature decreasing the survival of all species, increasing levels of tissue necrosis and bleaching, elevating respiration rates and decreasing photosynthetic rates. OA alone had little adverse effect, even under RCP8.5 concentrations. Importantly, the interactive effect of OW and OA varied between species with different nutritional modes, with elevated pCO₂ exacerbating temperature stress in heterotrophic species but mitigating temperature stress in phototrophic species. This antagonistic interaction was reflected by reduced mortality, necrosis and bleaching of phototrophic species in the highest OW/OA treatment. Survival and settlement success of Carteriospongia foliascens larvae were unaffected by experimental treatments, and juvenile sponges exhibited greater tolerance to OW than their adult counterparts. With elevated pCO₂ providing phototrophic species with protection from elevated temperature, across different life stages, climate change may ultimately drive a shift in the composition of sponge assemblages towards a dominance of phototrophic species.