Swiss banks reject Americans because of US legislation, namely FATCA (https://home.treasury.gov/policy-issues/tax-policy/foreign-a...) Foreign Account Tax Compliance Act. It's introduced reporting requirements and thus massive costs in having US citizens banking with you, thus it's cheaper to just say no. Rational economic response.
To be clear: The issue with FACTA is that saying "yes" to an American citizen (or national) adds costs to the foreign bank (in free labour on-behalf of the US). The US doesn't fund any of the work of reporting these accounts back to US.
Its almost as if the US has internal sources of free labour and expects no repercussions from expecting the same from their international counterparts...