They can and do co-occur, and might support other living systems. They are crucial for identifying environments and microorganisms on Earth that can be used to assess the possibility of life elsewhere, and to help design instruments for detecting that life. We believe the possibility for living extraterrestrial microorganisms depends on presence of both liquid water and a ready source of chemical energy. While liquid water is absolutely essential for life as we know it, mere presence of liquid water on another solar body does not imply that there is life. There is evidence for liquid water deep in the regolith on Mars and possibly below the ice layer on Europa.
Microorganisms use light or chemical energy.
Presumably this is the case for life elsewhere. Earth-like photosynthesis is unlikely elsewhere in our solar system. We must therefore search for non-photosynthetic life. To do so we must know what energetic systems to look for. Astrobiology considers microorganisms that can utilize chemical energy sources, and especially anaerobic microorganisms.