I wonder who is doing the appeasing...
The country being threatened or the conglomerate doing the threatening. Iran isn't making any demands on the West for us to appease them.
The protests are wholly internal. They mistakingly are presented in the West as a kind of revolt, a pro-Western revolt. But it's not the case. Mousavvi is the Supreme Leaders' brother-in-law, he studied Islamic Architecture at University and is very much part of the establishment. If you watch the Presidential debates on Iranian TV, the main issue was economics and corruption, not nuclear power, which a vast majority of Iranians according to most polls, are fully supportive of.
But Iran needs to evolve from the one party state. The clerical elite will have to change in many ways to reflect the population more accurately. Coups, forced change does not work for the Persians, not for long. Whether this is the Shah of earlier times, or the Islamic State brought about by the Iranians themselves, they as a people eventually decide when a change is needed.
Hopefully it should involve as little violence as possible. I'd say in comparison to Britain governmentally, they are in about the....1900s. But with twitter and mobile phones it shouldn't take a century hah!