Our oldest would have gone to first grade this year. School started on September 1. I started our "homeschool year" the same day, for two reasons:
First, the girl next door went off to first grade on the bus and our son didn't and he felt odd about it. He had previously been teased by a different neighbor kid that he "didn't know anything because he doesn't go to school", and I wanted him to feel like his homeschool was every bit as much of a serious big-kid thing as it would have been to go off on the bus. The first day of school is hard to not notice here - we live in a cul-de-sac and the bus stops at the mouth of it and on the first day, three families of parents and their kids were all gathered outside to see their kids off - it was a big deal that we couldn't not notice going on - so I felt I needed to make a big deal about DS1's "first day of first grade" as well. And it was kind of cool how ready he was to get to work after the bus came each morning for the first two weeks ! So starting a new routine at the same time as the neighbor kids worked out well for us.
The second reason is for record-keeping. It's not required here, but I choose to keep pretty detailed records by date and subject of what we do. I think starting school on the same day as our district looks good on paper...but I have no plans to stop for the summer, so our "first grade" records will continue up to the first day of school next fall, when I will start a new set of records for "second grade".
If I have new materials I really don't want to wait to get into, since I'm not stopping for the summer, I would go ahead and start using them. On the other hand, if I have something I want to introduce, either a new material or a new routine, and it might be helpful to have the beginning of a "new school year" to use as a dividing point to start something new and to add a little oomph to it, I might use the beginning of the school year for that.