How do you interpret the final scene?

The scene sets the basic dichotomy inherent in the American Western, between Civilization and open spaces of the frontier. The former is where we live, it's the culmination of the American Dream, the conquering of the wild, turning it into a place of law and order. The latter is where a man can be Free.

Ethan is introduced at the beginning, coming from the frontier, as WE watch from inside, with the family, from inside modern civilization. The closing scene echoes that. Ethan has returned, with Debbie. She's embraced by her family, and they enter the home, as the camera back-tracks inside. Ethan walks up two steps, and moves aside, making way for the young couple, the FUTURE.

Ethan understands that he has no place inside, within the Civilization. He can't exist by other people's rules. He needs his freedom. So he turns around and walks off, as the door closes, leaving US there with the family, our place, in 1956 (and now).

Ride away, ride away.......

"What can be asserted without evidence can be dismissed without evidence."

I dont think it has smth to do with violence or polite society but I like your thinking.
I think it has smth to do with civilization itself. With culture. Martin is part "indian" himself and he gave up that culture, that part of his identity completely to "fit in".
John Wayne is just the guy who gets things done. This is his identity. Doing what needs to be done. Not good nor bad. Slavoj Zizek talks about this. If civilization gets so "evolved". Civilization needs "sociopaths" that can act outside moral standards, ethics etc. to protect civilization itself. That is why figures like Tony Soprano, Dr House, Dexter or Homer Simpson are so popular among our society. But we really wouldnt want them at our dinner table, do we?
That indoor/outdoor shot is the cinema itself. All the people of the movie practically come into the theater room. Among our civilized midst. John Wayne stays out. It makes me sad that there is no room for individuals in civilization. We claim to be tolerant but the truth is we are not.

He's getting old.

He has bequeathed Marty his property. He must also realise that he is bequeathing Marty the authorship of his legacy.

Ethan and his attitudes are a product of his experiences. He is also self aware, to a degree.

After his odyssey, and in spite of his prejudices, does Ethan really want his life to be defined in the end as a spiteful child killer? Like some ironic footnote or a lesson from Greek tragedy? Or does he want to be someone likely to be remembered as a worthy set of bones that the spreading nation had to be built upon?

That obsession with creation of a legacy is a defining characteristic of the growth of the American nation.

"Who can't use the Force now?! I can still use the Force!" - Yarael Poof

Ethan spent 8 years away fighting wars and then many more years tracking and killing anyone who got in his way on his search for his niece. I thought it was made apparent from the beginning of the film that he had no interest in cattle ranching or settling down. And since his closest family had been killed off, he really had nothing to go back to. Removing Debbie from the Comanchee one way or another was all he had left to do with his family. Once it was taken care of, he moved on to another chapter in his life (probably tracking or killing or fighting some more).

All great stuff. But it could just be gestalt, like how Ethan picks up Debbie at the beginning of the movie and at the end. The movie starts with the door opening. It ends with a door closing.

Ethan stays. He is needed. The Jorgensens are older and newly burdened with Mose Harper and Debbie. Laurie and Marty will marry but start out poor as church mice. Ethan will rebuild the ranch and help prosper the cattle to the benefit of all concerned.

Ethan is bent on killing Debbie by the time they catch up with Scar. He's been constantly telling Marty he isn’t his nor Debbie's kin on account of his mother's Comanche blood.

Even though he can't bring himself to kill Debbie in the end, it must surely not sit easily with him, the idea of Debbie being accepted in the Jurgensen's family even though she was never their kin and has been with the Comanche for years.

I think Ethan is confused and lost in his prejudice and distrust.

I interpret the closing shot as a sad scene. Notice how nobody seems to pay attention to Ethan as he stands there. Nobody looks at him. Nobody nods at him. Nobody says thanks or anything to him. Nobody invites him in. Debbie goes in with the lady and the old man. Martin and his girlfriend go inside, walking right past Ethan as he looks at them … Ethan really does seem all alone. The viewer is left to wonder what’s next for him: Ethan himself probably doesn’t even know

I think the final scene was meant to be a commentary on the Western hero. We admire Wayne in this movie (and all his other movies) for his bravery and toughness. But the lifestyle that made his bravery and toughness possible also prevents him from having a good life with family and domesticity . The movie may be saying that the Western hero isn’t all that great in the end. You’d rather be Martin at then end than Ethan