In Teaneck, the cutoff is September 30th. I had a son on September 17th.
In the younger grades, sometimes kids aren’t emotionally mature enough to start. A lot of people have told me that their 4 year old wasn’t ready for school so they kept him back. I’ve been told that girls generally stay in their grades but boys often get held back.
My philosophy is to examine it based on the child. My niece was pushed ahead (she was 2 weeks past the cutoff) because she was ready for school. Each kid is different.