Church has enough problems without becoming a battlefield for racial quotas and litmus testings. Send the sort of pastor who will easily fit in. If this is a congregation that has made it known that they wish to try someone of a different background, then send such a graduate to them.
If too many parishioners are not comfortable with the graduate theologian, most will simply stop coming to that church. Then everybody loses.
I used to be a Fundamentalist Protestant and the whole racial hang-up has always been stupid. It flies in the face of monogenitic, literalist creationism and chrstianity's claim to be the one true religion for everybody in the world. And once upon a time--when the lynchings and church burnings were at their very apex--Black chrstians were actually Fundamentalist. If the two ethnic groups had made some sort of move to unite on a common theology we wouldn't be in this mess today. Unfortunately conservative whites at the time would have nothing of it and the entire Black church since seemingly made a collective decision to switch to eighteenth century European "enlightenment" rationalism and nineteenth century European materialism.
There is no need to feel uncomfortable because of a co-religionist's color or ethnicity. It is always a minister's theology that has to be watched vigilantly.