Don't over analyze things, especially when it comes to a man's motive.
I watched the movie but haven't read the book.
The way the movie goes, it is about a grown man, still a cowboy in his own mind.
Some people are born protectors. Their protective nature overshadow everything else.
Chris Kyle seems to be such individual. He might not even comprehend the big picture from a political point of view. From the stress of war where he witnessed his friends being killed, it is solidified in his mind that his people, fellow American marines and seal lives are under constant threats. And in this situation, the mind goes into survival mode most of the time.
It would take a long time for him to think otherwise. Yet he did hang out with former marines and help out. He was really good shots and might took a long time, and some really good friends to let him learn more about himself.
Too bad he didn't got the chance.
Don't be too harsh on this guy. He did try to help. And those lives that he saved, they would see it that way.
A lot of tribes have stories of warriors. And maybe it is not sophisticated enough for the more modernized audience, it is fine to see it as an good old fashion warrior of a tribe.