I'll add my counter-anecdote: I'm a US citizen with an ordinary (non-diplomatic) passport. I visited Iran twice to give talks at research meetings, both during

I'll add my counter-anecdote: I'm a US citizen with an ordinary (non-diplomatic) passport. I visited Iran twice to give talks at research meetings, both during the period when sanctions had been relaxed under Obama. I was worried that having the full-page visas in my passport would result in headaches at immigration to various countries, but I've visited 15 or so countries in Europe, Asia, Oceania and the Americas since then and never been asked a single question about it. (Your mileage may vary.) Anyway, I tend to believe the German authorities on this one.