Global warming, globalization, industrialization, and the rapidly growing population at present increasingly affect the production of safe drinking water. In combination with sustainable bio-based or recycled materials, used for water distribution systems, these factors promote emerging pathogens, including fungi. They can proliferate in oligotrophic water systems, affect the disinfection process, degrade building materials, and cause diseases in humans. In this study, we explored fungal-based degradation of modern concrete water storage tanks and the presence of fungi in chlorinated drinking water at the entrance and exit of the tanks. The degradation potential of isolated 52 fungal strains and their growth at different oligotrophic conditions was tested in vitro. Forty percent of strains grew at extremely oligotrophic conditions, and 50% classified as aerophilic. Two-thirds of tested strains produced acids, with Penicillium strains as the best producers. Only 29.7% of the strains were able to grow at 37 °C, and none of them was isolated from drinking water at consumers' taps. Although not yet part of the guidelines for building materials in contact with drinking water, fungi should be taken into consideration in case of visible degradation. Their number of consumers' endpoints should be checked to exclude possible health risks for consumers.