I'm a tutor, and I have a lot of fun doing it, so I filter a lot of information I get about "what works with people" and "how to change situations" through my experiences there.
And I agree, it saves a lot of energy and pays off to greater effect when you don't fight culture.
For me, that means, when I go into a home, finding out what the culture is in the home. The kid I'm tutoring has a dynamic with adults, with other people. Part of my job is to suss out that dynamic and work within it.
That can mean a lot of things - acknowledging when I make mistakes or NOT acknowledging when I make mistakes. Basically, I gauge off my student; does this person seem more or less tense after I've acknowledged that my analogy was silly, or that I've made a clerical error? And then I adjust to that.
My goal is to maximize the time that the student spends engaging as directly as possible with the material. Culture clash is distracting. I try as much as possible to observe household culture in order to fit in as smoothly as possible.