This is a huge mistake by the media as the woman could be ill. Second, it's crucial for patients to be able to choose. 

If she is well, a racist rant is clearly wrong but she is nevertheless entitled to choose a doctor she feels comfortable with - and this includes, everything from gender, religion, culture, outlook. I have never thought about race being an aspect, but if that is her comfort level, she has a right to make the choice. We don't know what her thinking is. It may be based on some past experience or not. Mentally ill patients often express racism and other similar fears, and must not be persecuted for it.

For example, many women choose female doctors as that is their comfort level. Many patients would reject religious adherents for fear of certain values. It's their right.

Putting an irate loud, clearly stressed, patient online or in the media for this is clearly wrong, on so many fronts.