Can anaerobic bacteria in your water cause health problems? If so what?

No. By and large they are harmless unless they get into the lungs, where they can occasionally cause lung infection. I would not be worried about this kind of bacteria in the drinking water.
Yes, all kinds-↓Odds. Anaerobic: bacteria which do not survive well or long under low oxygen conditions, thus not common in water exposed to the air for long. There are hundreds of thousands of different types of anaerobic bacteria, many routinely living in our colon off when we do not absorb or shed & outnumbering aerobic bacteria. We are well adapted to many, collectively called the human biome. Thus no simple answer.