There's a rather small but critical lack of nuance in your sentiment.
The idea isn't that you judge the person because of their skin color. Nobody is saying being white or black makes you a worse or better counselor or person. The idea is that you merely judge the likelihood that the person will be able to relate to you about something in your own personal life. There's nothing "problematic" about making that kind of judgment. It doesn't need to be justified or rational to anybody else. It's your personal life that you're looking for someone to open up to. Nobody else has any right to anything in your personal life, and you have every right and responsibility to make it better by your own criteria. If there's any problem here, it's the sentiment that other people have a right to dictate whom you should and shouldn't involve in your personal life.
But doesn't that mean race can potentially become extremely important when the treatment is via a form of structural socialization?
An emotional barrier that is part of the problem for which a person is seeking treatment:
(1) is not a judgement, and
(2) indisputably is part of the problem.
But, in any case, whether either or both of those are true or not doesn't change the fact that it is a real issue impacting the likely treatment outcomes that is sensitive to whether the counselor is in the group triggering the negative response or not.
This is not to say that you shouldn't judge a counselor by their behavior after you've started working with them. But I think it's possible for a person with black skin to be just as insensitive to the concerns of black people as someone with white skin, e.g. Clarence Thomas.