Have been waiting to see replies and had expected someone to to repeat earlier recommendation to have your son speak with his coach and get an indication of his current role and what he can do to gain more playing time. The veil of politics, IMO, begins to lift as players migrate to varsity and the coach decides to play the very bet kids based on his assessment. You did mention having moved several times so I assume the current coach does not have an extensive history with you kid, but may have worked with other juniors and seniors for several years. there will be some level of "loyalty" where if your kid is tied with another kid who grew up in the program, that other kid just might get the nod.
No offense, but your comment about the one at bat has little to no bearing on the discussion nor does what the "other" parents are saying (they may just be really nice folks or have kids that are in a similar situation). During his AB, he apparently had three teammates get on base ahead of him to allow his RBIs, so they should get most of the credit. He does not need a coach's recommendation in most instances (assuming you are referring to HS coach) and summer ball will largely drive the recruiting process.
Maybe some info on where he plays versus other established players on the team. Your kid, as the newcomer, needs to demonstrate - to his coach - beyond doubt that he can contribute more to the team's winning than some other player. If your kid can gain an appreciation for what his coach likes/dislikes about him and how this stacks up against others, then he can work towards convincing the coach and highlight the attributes that are desired and diminish the attributes that are not.