People in the clergy are not only obligated to members of their flock or congregation, but to be truly Christian, they should service society as a whole, and that includes members of the general public and people who practice different religions or don't even have faith in a higher power at all.
Yes, it is important for clergy persons to have cultural competence when working with the public or those not of their faith, because they have to serve everyone. It is important for the church to be culturally competent in order to serve the needs of the variety of people who interact with the church.
I believe it is important for clergy to have cultural competence when working with the public or those not of their faith. Cultural competence simply means the ability to interact with those from different cultures and different socio-economic backgrounds. Clergy should be able to do this quite well or not take up the position at all.
Religious leaders need to be able to approach and respond to multiple publics, not just the group of faithful that they have chosen to serve. When clergy are only able to speak to communities of believers, like minded individuals who already agree with one another, this is simply preaching to the choir.