If you knew your shortlisted Private & reputed maternity hospital has high cesarean birth rates vs a decent Government hospital, would you change your mind?

I think it depends on the gynae himself/herself whether he/she is pro-natural instead of relying on the hospital's c-section statistics. Normally a gynae has protocols on whether to proceed to c-section, e.g. when baby is in distressed or high risk pregnancy. Under normal situation, most of the gynaes will let you try natural birth. You might want to search online and read up reviews on your choice of gynae, whether he/she is pro-natural birth.

I agree with @diana, I would focus on the gynae rather than the hospital. I am sure you must have done your research before choosing a particular gynae. Over the course of pregnancy, both of you must develop complete trust in your gynae to make appropriate decisions. If not, then I would recommend changing. Hope it helps!!

My main concern would be picking out the doctor to handle delivery. So I defer to his/her judgement on hospital or facility. I'm not predisposed to c-section or natural birth either so the c-section birth rates don't matter as much to me as my future baby's safety. Whatever is best for the baby!

When I had my first pregnancy, I just listened to one of my co workers recommended OB Gyne which she highly preferred. For me it would be OB first, second the hospital itself if it has complete facilities etc.