I assume you are right that both AMD (partially owned by the United Arab Emirates [1], 1/3 owned by a Chinese company with strong ties to the CPP), and Intel (wholly owned by an American private company, but who does a lot of its development in Israel) both have back doors. I further assume that every chip made in Taiwan and in China has a back-door as well.
I don't know of any real solution, but maybe Framework will one day make a verified chip, and maybe there will be a way to audit it?
In the interim, as much as I allow the back door to affect my purchase, I still trust Intel more because: 1. As bad as the U.S. is in telling companies what to do, China and the Abu Dhabis are far worse, 2. I suspect the U.S. are less likely to use the back door against me. 3. Intel intends to do a lot of manufacturing for other companies, so there is a greater chance of catching hanky-panky.
[1]: Through its merger with GlobalFoundries, which was "spun off" but still has partial ownership and still does all the actual chip production