Sponges, and corals, too, do not have intrinsic color. They are naturally white or light grey.
However, their tissues are colonized by symbiotic microorganisms which do provide coloration. In corals these are an algae, specifically zooxanthellae. In sponges, including barrel sponges, they are a bacteria, specifically cyanobacteria.
Bleaching results when these microorganisms are lost due to pollution, abnormally high water temps (such as are caused by an El Nino), direct physical injury (such as results from divers grabbing them) and similar trauma.
While bleaching is becoming distressingly common, and may be accompanied by a reduction in size and increased susceptibility to predation by creatures like parrotfishes, it is only rarely fatal to the entire sponge.