Now here is the question. Should T respect:
a) The patient's culture?
Absolutely!! A T should be culturally sensitive.

b) Her own culture?
Yes. The T should not do something that makes her terribly uncomfortable. For example, since you specifically mentioned touching, if the T does not want to hug a patient, for whatever reason, the T should not hug unwillingly. That would be a disservice to the client anyway, and inauthentic. I think a patient would be able to feel if the T was forcing herself to hug and that could be damaging.

c) The dominant culture of her practice?
For patients from that culture. But not for other clients. If most of the T's clients are one culture, the T should not apply the cultural mores of that culture to other patients that are not of that culture. The T should be culturally sensitive to all cultures. (Perhaps I didn't interpret that question correctly?) One also needs to be aware about assumptions about culture. For instance, some European-Americans are very huggy and some were brought up to be more formal and not touch as frequently, especially those they haven't known for long. And the moniker "Asian" encompasses dozens of very different cultures. So the T has to meet individuals where they are and not automaticallly assign his/her preconceptions of what their culture is like.

BTW, in my current health care training, we have a lot of emphasis on developing cultural awareness.