In worldly transactions such as business, science, and medicine, Muslims and non-Muslims are almost the same since it is their knowledge and expertise which are of value. You should search for the most qualified physician, the same way you would search for the most qualified and knowledgeable driver if you needed to get somewhere.
There may be a few reasons to prefer a Muslim physician over a non-Muslim. People generally trust the advice of their doctors, even though medicine is not always an exact science. A Muslim physician who is knowledgeable about Islam may therefore be able to give better advice about medical issues that affect Islamic moral values such as abortion, sterilization, etc. For example, when a Muslim asks their physician whether it is safe for them to fast in Ramadan, the answer given by a Muslim versus a non-Muslim physician may be significantly different. This is because the Muslim physician understands the importance and value of fasting in Islam and will therefore generally encourage fasting whereas a non-Muslim might discourage it. There are many incidents of this happening. The second reason to choose a Muslim physician would be to help recirculate money within the Muslim community, making Muslims stronger and more prosperous.
Shaykh Mustafa Umar