Why didn't Sean go with Toretto and the gang?

At the end of Tokyo Drift, Sean is still in school. As the end of Tokyo Drift links in with Furious 7, Sean would still need to complete school.

Whilst the crew aren't known for their general abiding of rules, I think they would agree that what they are up against would be too dangerous for a kid, and that he'd be better off staying in school.

Others have also mentioned that Dom wouldn't know him or his true abilities, and he likes to keep things within his own trusted family; which Sean is not part of.

For an in-universe answer, the first draft of Furious 7 (then titled Fast & Furious 7) actually featured Sean coming to Los Angeles to work with the crew, much to Roman's dismay as he didn't believe in drifting or that a kid was friends with Han. However, his entrance did not involve going to Tokyo, and rather ending with the hospital scene with Dom announcing he's going to Tokyo, it cross-dissolves to the funeral, where Sean is present and crying.

Roman asks who he is, and claims he didn't know Han, but Tej backs up Sean, claiming how they "rolled together" in Tokyo. And Sean tells them that Han was his friend and wanted revenge.

Roman continues this rivalry, even trying to make sure Sean wasn't with them when they drove their cars out of the plane. But by the end of the film, he accepts him as part of the family.

(Fun-fact, Hector was also going to be the main character, possibly these two to replace Han and Gisele).

Well personally I would've enjoyed this, this wouldn't have worked out as Furious 7 and Tokyo Drift link up, meaning that Sean would've still been 17 and thus not allowed back in the US.

Why they ended up removing this plotline I'm not sure, but potentially it's due to the same reason why Black wasn't in The Fate of The Furious, because of scheduling conflicts with NCIS: New Orleans. It should also be noted that Black will not be returning to Fast 9 either, despite the news that he signed the contract for three films.

Potentially Black will be in Ten and we could get a spin-off about what he did after Tokyo Drift, but these are just faint-hearted hopes.

This video here helps explain what I've mentioned here, as the user bought a copy of the original script and it's confirmed that what is in it is true.

IMO, I think Sean was so far removed at that point, and Dom already had his current team in place. They all worked together in Fast 5 and 6, and Dom didn't really need "just" a driver (which was all Sean was). Bringing him in kept the continuity, but there really was no need for him on the team in F7. Besides, no one but Han really knew him well.

Sean anyway wasn't aware of the whole toretto-shaw rivalry. For him death of han was an accident which was a result of ugly car chase. Sean was a normal school guy who got a bit too much involved in racing , involving him in any other sort of things (LIKE FIGHTING A TANK) would've put toretto and his family in jeopardy.