I have relatives in the US in a similar position [...]
If these people were to swear to defend the US they could become citizens. Then if someone demands they actually do some defending they explain they are pacifists and they'd be OK. Nobody would force them to fight because US laws on conscription etc. recognise conscientious objector status.
In other words, the arm of the US government concerned with demanding violence from its citizens (the military, etc.) doesn't mind them declining to commit acts of violence, but another arm of the government (the citizenship authorities) does mind because it feels obliged to protect the interests of the first arm. The second arm is being overly zealous, providing assistance beyond what the the first arm wants or needs, and causing unnecessary side effects in the process.
The moral of this story is that there's a bug in the citizenship procedure. Conscientious objector status ought to extend to the citizenship laws as well - someone who can prove conscientious objector status, to the same standard as demanded by a conscription board, ought to be allowed to swear a citizenship oath that does not demand defence, at least not in a violent way.
Caveat: Assuming the parent's information is all accurate.