There is an important point to be made about Rabbah's statement. The purpose here is not to teach us that it is forbidden to reveal information that would in any way cause monetary damage, or that can be construed as being negative or unflattering to any of the parties involved. That we would have already known from the laws proscribing evil speech and tale bearing (hilchos lashon harah v'richilus). Rather, Rabbah is telling us that any private conversation must not be repeated to others without first obtaining consent, no matter how innocent the conversation may seem to be (see Sefer Chafetz Chayim, hilchos lashon harah, klal 9).
Of course, to correctly apply this high standard of confidentiality to a specific situation any countervailing priorities that may exist must be added to the halachic equation. As always, when in doubt a competent halachic authority should be consulted. Be that as it may, the fact remains that from Rabbah's teaching we can conclude that maintaining a very strict level of secrecy regarding a client's information and conversation is certainly a Torah ethic.
Does this ethic override a call from Beis Din to divulge privileged information regarding one's client? The answer is an emphatic no. Numerous authorities make the point that even if one explicitly promises to someone not to reveal his secret information, that promise does not relieve him from the obligation to testify in Beis Din if called upon to do so. Even more, a person's duty to fully disclose whatever information he has to the Beis Din exists even if the person swears in Hashem's Name not to testify (see Choshen Mishpat 28:1, Pischei T'shuva s.k. 3, and Shu"t Tzitz Eliezer, 13:81).
The reasoning behind this ruling comes from this week's Parsha. In Vayikra 5:1, the pasuk states, "And when a person sins: and he heard [someone's] voice who pronounced a curse [on anyone who knew information about his case but would not testify] and he was a witness - either he had seen or he had known [something about the case] - if he does not tell [what he knows], he will bear his iniquity." The Rambam in his Sefer HaMitzvohs understands this pasuk to be placing a positive commandment upon a witness to testify (positive commandment #178). However strong the Torah ethic of client confidentiality, it pales in comparison to a full-fledged positive commandment. There is a halachic principle that a person who makes an oath (shvuah) in contradiction to the mandate of a positive commandment is not bound by the oath. Rather, the Torah's directive is preeminent. Thus, even making a shvuah of client confidentiality will not exempt one from the obligation to testify.
It would seem from our discussion so far that the client of a Torah-observant Jew should be rather wary about the fact that the Torah does not seem to recognize the legal concept of 'privilege.' There is a likelihood that if a client will become involved in a law suit in Beis Din, his Jewish lawyer, accountant, or doctor will be obligated to testify if called to the stand. There is, however, one more halachic angle regarding this subject which significantly effects what actually will happen in such a situation.
In his work Avkas Rochal, siman 195, Rav Yosef Cairo, the author of the Shulchan Aruch, explains that the mitzvah to heed the call of Beis Din to testify is essentially an obligation to act with kindness to one's fellow man (gemilus chesed). It is simply doing a good deed for the person on whose behalf the testimony is being given. In this way it is similar to such commandments as returning lost objects, visiting the sick, and giving charity. According to the Avkas Rochal's view, the mitzvah to testify at its core is not seen in halachah as an inviolate obligation upon a witness to see to it that 'justice is served.'
Mitzvohs of gemilus chesed are different than other mitzvohs in that they do not need to be performed if a significant financial or personal loss will be incurred. For instance, one does not need to return a lost object that is relatively inexpensive if it will mean taking time off from work since one will not likely be able to recoup the lost wages. Based on this principle, the Avkas Rochal rules that Beis Din cannot force a person to testify if doing so will cause significant financial or personal harm to him.