In our district, accelerations and skips are handled in the same way: only at the parent's request, and based purely on testing. It makes it really hard to not look like a pushy parent with a higher-achieving kid.
When DD skipped 2nd, I had a long discussion with her first grade teacher before we decided to attempt the skip, and one thing her teacher said was that there were several kids in DD's class who were ahead enough to skip. So I played up that idea when I was talking to other parents. The kids came up with it all on their own - "I could have done that if I'd wanted to" was the most-common reaction DD got, even from kids who give no sign of being high achieving.
Particularly in K and 1st, there's enough spread in achievement that my kid did not stand out as unusual. (Her first grade teacher said the reading abilities of kids in her class spanned 9 grade levels, and my DD was not the best-testing reader.) As the kids get older, though, she stands out more. If she does a subject acceleration for the coming year (as a 5th grader taking one or more 6th grade classes), I don't know that there'd be any "I could have done that if I'd wanted." OTOH, I don't know that any of the kids would be the least bit surprised that DD was doing it.
