when in fact he should not be considered Jewish simply because he is on a technical level
Not sure why the “technical level”, i.e. halachah, isn’t important to you.
On a technical level, Im sure there have already been US presidents who are Jewish as well- we just don’t know they were Jewish.
I’m sure not, because halachah does not assume someone to be Jewish without a chazakah.
As an aside, no president, AFAIK, has ever claimed to be an atheist, so my point would still stand.