Reference: Ghaaratul-Ashritah ‘alaa Ahlil-Jahli was-Safsatah – Volume 2, Page 192
Question: Is it permissible for a [pregnant] Muslim woman to go to the hospital to have her child delivered whilst she knows those who will be delivering the baby will be non-Muslim men?
Response: If the situation necessitates, there is no harm in that if she is unable to find anyone other than non-Muslim [men]; We have read this is not permissible for her except with a Muslim doctor, however, where is the evidence for that? And [we know] matters of necessity have rulings specific to them.