Most schools assume boys are behind girls developmentally, and any boy with a late birthday will be even more so. That doesn't apply to gifted kids, as you noted. I think most gifted kids, even if they may seem to struggle socially at age 5 or younger, rise to the occasion and prefer older kids by around 1st grade on up, if not earlier.
My DS7 (January bday, so no age cutoff issues) is one of the most mature kids in his 1st grade class and gets along best with the brightest kids in his 1st grade class and the 2nd graders he takes math with. He would easily fit in with the 2nd graders if we needed to go that route. Also, if athletics are a concern for you as some responders noted, some districts like ours run athletics through county-based leagues rather than through schools and perhaps you have those options too.
My brother and SIL red-shirted my gifted nephew on the advice of his school. He's only 7 months younger than my DS (August bday). He's really having a hard time in Kindergarten this year, acting out, bad behavior, and he's bored. I should clarify that DS and nephew are in the MG range. They were not (and still are not) reading at a 3rd grade level at age 5, and we're still seeing the maturity and preference for older/brighter kids. That will be even greater with your kiddo who is more advanced.
A bigger concern for me if we were considering grade skipping would be middle school years. Others on this site have talked about having a hold-over year around that age. Our district offers so many options for advanced kids from middle school on up, that it's possible to put a grade-skipped child into middle school where they're mixing with several different ages in advanced classes, and it becomes less of an issue. Overall consensus I've seen on this site about grade skip worries for later years is "do what works now and figure out the rest as you go."
Welcome to the site, the parents here are a wealth of knowledge!
