You assessment of the law, in my opinion, is not accurate and counter-examples to your assessment have already been provided.
The law does not project all attributes legally (it applies different standards of scrutiny to decide whether equal protection was violated), and there are numerous examples of where legal discrimination against one of the attributes is legal while it is not legal to discriminate against all attributes (handicapped parking spaces, washrooms, purchasing alcohol, retirement plans, pastors). You cannot simply say that because you can (or cannot) discriminate based on one class that it applies to all other classes as well.
While I agree that the person is free to choose who they are served by, I believe that 'who they are served by' in this case is choosing what hospital to go to. I disagree that because in this specific case the woman was not harmed that there is no potential harm based on the hospital providing this accommodation, or that the potential for such is not meaningful from a legal perspective.
I understand that this is taking the form of a slippery slope argument, but there are numerous historical examples where this end point was realized, which is why these laws exist in the first place. When it is okay, legally, to allow certain races of employees to serve 100% of patients but other races to serve <100% employees, it is breeding the conditions for people to be harmed.
Think of segregated washrooms. A mall may institute this and provide exactly the same accommodations for all races, in which case no race is technically harmed up to that point. The problem is it greatly increases the opportunity for harm to occur, which is why if it is challenged it likely would not be allowed.