How can we eliminate stress on students learning a new dialect?

It is clear that there is a higher stress level put on students with a dialect other than that being taught. It is difficult to leave the comfort zone or to feel free to express oneself when being criticized constantly and not experiencing improvment. Delpit notes that when writing it is often easier and less stressful for students to use rules of a new dialect, where there is no room for revision before scrutiny in orality. Delpit also notes the ease with which many people pick up a dialect unconsciously vs. trying to consciously learn a new dialect. How could we as future educators work to eliminate this kind of stress from the classroom? Besides being conscious about making corrections, what could we do to emulate this “unconscious acquisition” of a dialect to help students learn? Do you even think this is necessary in a world where diversity is spreading, to conform every student to the “standard English” dialect?