This oath is still taken by all physicians today. The first bold text section means that they will treat any condition they can to the best of their ability and the best of their judgement. The second section says that the physician will keep secret anything that you bring with you into his office.

So, a physician might recommend someone get psychological help, but he cannot refue to treat a patient because of whatever lifestyle that patient leads.
Unfortunately, in some states (in the U.S.), a doctor can (and must) under law report what they would consider evidence of abuse. Not all places are like that but some very much are. Just as in some places if the police get called for a domestic disturbance and they see bruises or anything they could consider abuse they not only have a right but an "obligation under law" to arrest the suspect for domestic abuse even if the "victim" refuses to press charges the state can press charges. Like I said, it isn't like that everywhere but it is like that in many places, despite oaths.