I have had a goatee my entire career. I have never been told to remove it. I have never been told that I should get rid of it if I move up. The only indication that I see of getting rid of it, is when I get to the D1 level. All the African-American Officials I see at that level only have a mustache. I have never seen a goatee. So if I want to go to that level eventually or go to those camps, I might have to get rid of it. But I have never had a lower level college or my HS assignors ever tell me to remove it.
I think it is cultural that more African-Americans or people of color have facial hair. It is hard not to find a Black male that does not have at least a mustache. Of course there are many that do not have anything on their face, but much of my generation does.
Interesting question.