If you are speaking especially of the stomach, it actually makes no difference because the extremely low pH of the stomach allows very few bacterial organisms to survive. Often, Helicobacter pylori can however be present. Whether dissolved oxygen makes a difference to it is, to my knowledge, unknown. However, pure water does not stay long inside the stomach and passes almost immediately through to the intestines in most cases, so I doubt it would make that big a difference.
Now, it seems you are actually referring to the intestines in your question. Well, in fact the bacteria that inhabit the gut are almost exclusively limited to the colon and to a limited extent to the distal part of the ileum (small intestine). The stomach and almost all the length of the small intestine are sterile. Water absorption takes place in the jejunum (proximal part of the small intestine), which is a sterile region proximal to the locations colonized by bacteria. In conclusion, the oxygen content of tap water will not influence the bacterial flora simply because it does not come into contact with those bacteria.
BTW, the major difference between tap water that you leave sitting and the one that just came out of the tap is the chlorine concentration (decreases with time). Of course this will favor microorganism development, since it is precisely one of the reasons why we put chlorine in the water in the first place...