And if tomorrow I tried to "choose" to become angry every time someone showed me a picture of a salmon, I couldn't do it - I could pretend to be angry, but I couldn't make myself feel genuine rage.

Actually, I think you're wrong about this. Pretending to be angry, offended, or sad has the effect of making one angry, offended, or sad, in my experience. Not as much as you pretend, at least at first, but it really can become genuine, even if you actually don't care about salmon at all, as long as you choose to pretend convincingly enough.

[Edit: ...but I see Vladimir M has already made this point, better.]

But drawing pictures of Mohammed offends many Muslims, not just the ones who send death threats.

I'm not sure that this is clear to most non-Muslims. In fact, I think that if you took a survey of Westerner non-Muslims, you'd find that they expect that Muslims more likely to (actually rather than ritually) be offended by such pictures are also more likely to send death threats.