Lightb, like Lilmod U said, circumcision is a Mitzvah and must be observed by anyone blessed with a new baby boy, with all details according to Halacha.
Cutting a little boy’s hair at three years, and then having him start to wear a yarmulka (and tzitzis in most cases) is minhag.
For those whose families have that Minhag it’s important to do it at the right time.
I haven’t noticed any pressure from nursery schools or play date parents to do this. Morahs, school administrators, and most observant friends you’re likely to come across know that it’s a Minhag, and will understand if your Minhag is different. It’s important to follow the Minhag if it is in your family so if there’s a doubt, a Rav or Poseik can help out the same way he can if it’s a din in Shulchan Aruch.
As for your saying that “one mitzvah or indicator doesn’t necessarily mean makpid on the others”- that’s a great observation, and something good to keep in mind, in E”Y, and across the globe!