There are at least two reasons why this is so.
First, our society today is a much more diverse place. Because of this, the talented people in our society today are no longer as homogeneous as they once were. Instead, there are talented people of many different ethnic backgrounds and nationalities. What this means is that any health organization (or any other kind of organization) that does not have a diverse workforce is likely to be depriving itself of talented people. If it is only hiring people of one group, it is missing out on many other good people from other groups.
Second, there is one factor that is more specific to health organizations. That is the fact that there may be people from different ethnic groups who are best served by members of their own groups. People of a given national or religious background may not be comfortable with the sorts of intrusive exams and questions that they have to face in medical situations unless there is someone of their own nationality of religion present. In this way, health organizations may be able to provide better customer service if they have a diverse workforce.