One of the most well-known parts of the medical doctors’ Hippocratic Oath includes a commitment to treating disease wherever it exists, and in whomever it exists. On a daily basis, physicians treat medical conditions for people who may have very different values than they might have, such as people who physically abuse their children, or people who may be racist. Thankfully, I am not a physician.
Psychologists have a bit more leeway in who they choose to see. If you have such significant bias against a person that it would compromise the quality of care that they would receive, it is ethical to refer them to another provider. That isn’t to say that you can refer someone out every time you disagree with them over something. You generally have to have a strong ethical case for refusing to treat someone (i.e., seeing them for treatment would cause more harm than good).
When talking about patients which I may have radical value differences with, one of my patients, Tom*, comes to mind. I enjoy working with Tom, for the most part. For someone who has endured severe chronic illness since childhood, he is a positive, upbeat, and compassionate individual. Most people in his situation would probably be severely depressed. On the other hand, Tom frequently shares beliefs with me that, unbeknownst to him, I am completely against. His views are often quite bizarre, and are generally a part of persecutory delusions stemming from trauma earlier in life.