October 1 for my home district in NJ. In this state, each district sets their own date, so neighboring towns could potentially have different cut-off dates, although 10/1 seems to be fairly common.
That seems unusual and is definitely not a statewide practice. In fact, a neighbor of ours here in NJ had their son in a private kindergarten program a year earlier than the district would have allowed, but he still enrolled in 1st grade in the public school even though he was younger than he should have been. He just started college, so this was quite a while ago.