Ethnic workers in ethnic industries

Do you think businesses that provide a service that is specific to a particular culture or ethnicity should have majority or only employees of that ethnicity?

For example: a Thai restaurant with majority Thai employees

Is it inappropriate for a person with no ties to that culture to start a business that originates from a different culture? Eg: me as a white woman, would it be inappropriate for me to open a Chinese restaurant even though I have no ties to China?