Hi Darek

They don't care. I go through whichever queue is shorter.

To make it even more confusing, some airports have signs which say "Non-EU passports" and others have signs which say "All passports".

A few weeks ago, I went into the "Non-EU passport" lane at Linate because the queue was far shorter. I was expecting to flash my US passport but I saw the gentleman ahead of me laid down a dark-red (EU) passport, so I showed my UK passport instead and the guard just waved me through. I would imagine it might be slightly different in Frankfurt.