Yes, it does matter what the cut off date is. Of course many August babies do just fine (I have:)) but the point is overall, they are disadvantaged in many ways, from being less emotionally mature, to being judged on SATS where they may have had almost a year less preparation than their peers.
The effect in the sports arena is covered in the Outliers book by Malcolm Gladwell. And it is also pronounced in other areas such as astronauts, exam results etc. The summer-born effect is well-known in education. It matters because people look at autumn born children and think they are cleverer, stronger, better at sports, more numerate or whatever, they get put in the top set, or picked for the team, and more time and energy is invested in them, so a circular effect is created whereby they really do become better over time.
It's also discouraging for parents of summer-borns when their children are compared with autumn-borns. I was chatting with a mum the other day whose child is not really reading much, only letters, she's just five, but her mum is comparing her to other children who are just six in the same class, who, nine months ago, may well not have been reading.
There is also something you can do about it: be aware of it so it doesn't factor in your decisions of who need help/who is very able; give more time and attention to the summer-borns when they arrive in school (which is just compensation for the time they didn't receive which the other children did) and so on.