Reading through anti-miscegnation laws from the 17th-20th centuries, many of them focus on whites and blacks inter-marrying. I realise that this is because it was far more common, but I'm curious how Native American and white marriages were viewed. Certainly it must have become common, especially in areas where there was a lot of mingling, like the Cherokee Nation. Were these also seen as "crimes against God?" Why did laws not extend to include these marriages?
It varies by location like all other laws. There were multiple anti-miscegenation laws that included Native Americans and Asians on the list of persons who could not marry whites. Mexicans are legally considered white in the U.S. so they could marry other whites but were technically off limits to other races in some states. Some authorities looked the other way though and in California there was a period when East Indian men married Mexican women to skirt other racist laws that prevented land buying/citizenship rights. Ronald Takaki discusses some anti-miscegenation laws in Strangers from a Different Shore.
During the French and Indian War, especially at British outposts, single common soldiers marrying Cherokee women was more common and wasn't as frowned upon as one would think.
For example at Fort Loudoun in Tennessee which was garrisoned by a South Carolina Independent Company, it is described in the book Indian Summer that many soldiers took Cherokee wives. It strengthened trade relations and served as a kind of diplomatic tie. After regional relations deteriorated and when the fort fell under siege in 1760, Cherokee wives even smuggled food and supplies in to their husbands.