Generally everyone except white people align along racial lines first. Within racial lines, things occasionally break down according to beliefs and values, but race/ethnicity tends to come first.

In a civil war, Indians would join whatever side intends to allow them to stay here, and that would trump whatever moral values they may have in common with white conservatives. It's why other typically socially conservative groups like Hispanics and Muslims traditionally vote more for Democrats despite not at all being aligned with leftist social values - the ability to stay here, and bring more of their own people here, is significantly more important than any ethical disagreement they may have. And all of them, regardless of background, feel more threatened and insecure about the "white supremacy" boogeyman than any ethnic conflict from where they're originally from.

A racial conflict in America would be half of white people against literally everyone else. Although having essentially only one group would probably be a strength in the conflict rather than a weakness.