You must consider a man's race if this concerns something relevant to that consideration such as their medical history. This is not one of them; there are actually very few instances where asking a man's race is necessary.
A lot of factors go into proper hiring and terminations, most significantly the merits of the individual concerned. Such factors will lead to an employee racial composition that might not mirror that of social composition.
Certain hiring practices like favoring women for flight attendants and black men for basketball teams should be terminated with extreme prejudice, but to force employee racial composition and specifically that one way or any other is racism.
I put an example of another way in my last post. If you're creative, you can think of more.
Another one is seeking out people and inviting them to apply, at which point they enter the normal unbiased hiring process.