Your own example...of the man in the military who is suing the armed forces for persecution; atheists cannot hold public office in many statess according to state constitutions, generally cannot hold office in Washington without at least paying lip service to Christianity; regular folk don't like atheists and are intolerant of them:
A few things:
1. The atheist suing the military has an experience that is inconsistent with those who have served, including me (a "religious" person) and HH6, who isn't really a "religious" person. It is unfortunate that some people are given a hard time, but I think that is the exception and not the rule. It certainly isn't part of any official policy, like you find in China.
2. You say "many" state constitutions preclude atheists from holding public office? Provide me with one reference. That kind of prohibition would be inconsistent with the First Amendment.
3. It is true that a candidate for the House, Senate, or president could likely not be elected if they were an open atheist. I think part of the reason is many folks don't trust atheists. They are the least trusted group in American according some polls.
None of this establishes that the U.S. oppresses and persecutes atheists. To the contrary, we actually protect them with the First Amendment.