I did not redshirt my August birthday DD (where we live it is not allowed anyway except in cases of demonstrated delays, or if you redshirt in private and then transfer for 1st) and it has been fine.
Her kindergarten year was, I think, more difficult than it would have been for a slightly older kid. That's the year when any differences in maturity are more pronounced. She's not immature for her age at all, but for instance when starting K she would still cry easily when upset, and her classmates who were 6-11 months older would not. But by the end of K this had evened out.
Academically it was obviously the correct choice. She was extremely ready and already reading without us doing any pushing (her PK teachers had her sounding out words and she just ran with it). She's 7 now and it's very hard for me to imagine her in a 1st grade classroom, where I think she'd be both way ahead academically and also much more socially mature. She's closer to the average where she is, which I think is more ideal.