Those who are following Rosh Hashanah, in the 7th Biblical month as the New Year, are following what was established by Judaism and the Rabbis. Those who are following January 1st are following what was established by Caesar. When YeHoVaH spoke to Israel in Egypt, He gave them a particular month to follow as the beginning of months, the New Year.
The Biblical New Year was instituted by YeHoVaH. We are commanded to observe the first month of the year and given Instructions on how to determine the first month. It is critically important to accurately determine the beginning of the 1st month of the year with the barley being Abib and the sighting of the renewed moon. That date determines the dates of the Early and the Latter Feasts.