That may be an issue when it comes to certain medical disciplines. Ob-gyn, for example. However, in the vast majority of cases there are few, if any, moral issues involved in medical treatment. What moral issues arise with setting a broken bone or treatment for high blood pressue?
So, your position that a Christian should not go to a non-Christian doctor is, in most cases, simple bigotry.
Well, as another person pointed out, what if the doctor was a Jehovah's Witness who disapproved of blood transfusions, while you need one. Or what if your doctor was a strict Jew or Muslim who refused to do work on the Sabbath, and therefore refused to help you until the next day?
So, your position that a Christian should not go to a non-Christian doctor is, in most cases, simple bigotry.
No, its a matter of associating with people who share your values and giving them your business, rather than supporting those who are undermining the type of society you wish to see come to fruition.