Even if it does literally mean 'death to America,' as an American I always interpreted that as being directed at the American government. I never took it personally. Hell, I could probably wear them out complaining about the federal government.
Also when the concept is paired with imagery of a Nuclear Iran, you can’t help but feel attacked.
My country has done a lot of stupid stuff in the Middle East. I get why they're upset. They should be. Fair enough.
It would be nice for us to move past the petty hatred over things that happened 50 years ago.