I`m not sure if I understood you corectly, If I didn`t I appolagize.
No, you didn't understand me correctly, but that's likely because I did not elaborate the point.
What I mean about my boy's situation is that I endorse that it will be their choice when they are grown up to be either an Indonesian citizen or an American citizen. While the US does recognize dual citizenship, Indonesia does not. At age 17 they are expected to make that choice. It's the freedom to make the choice that I endorse.
As to whether or not they are regarded as Balinese by other Balinese, as I wrote, that has a lot to do with how they are raised. Currently they are being raised as Balinese. They share in all the local village activity, temple ceremonies, and speak Balinese, as well as Indonesian and English. So, as I wrote, so far, so good.
In Bali, the culture is that the woman follows the man. When a Balinese woman marries a Tamu, she is regarded as having left her village, even though she still lives in the village of her birth.
As for patriotism, that has nothing to do with why it's impossible for a foreigner to "become Balinese." Even other Indonesians who have lived in Bali for many years never become Balinese. Racism has nothing to do with it either.
As for Balinese learning from other cultures, I would have to say yes and no. I see as much negative influence by the West or Australia on the Balinese as I see positive influence.
If you can, get hold of a copy of a recent book titled Bali, Living in Two Worlds. Its a compilation of essays written by Balinese on exactly this topic. It is edited by the wonderful Swiss scholar, Urs Ramseyer. Reading the Balinese opinions on this topic will be far more enlightening than reading my opinions.
Selamat hari raya Nyepi!