Like you, I believe there should be separation between governing the country and religion. But what about the situation in a free and democratic society when people elect groups that are related to religious groups, as happened recently in Turkey? Do we have the right to say your vote shouldn't be counted because you voted for a religious group? Do we have the right to say that the rest of the people should think like us? Obviously, no. Therefore we have to find another solution for this matter.
What I have found for that is a different definition of democracy. Democracy means governing by the majority. Please don't forget that many of these dictators reach their path through democracy. Therefore democracy cannot be without any limitations and control. Democracy has its own framework. It cannot be out of that frame, and the frame of that is respecting human rights. Governments do not receive legitimacy just by the vote of the people. A combination of the vote of the people and respect for human rights can give us that legitimacy. Therefore even religious governments should also respect human rights.
This is where we as Muslims can play a major role. We can prove that Islam is not against human rights and democracy. This is all challenged with the government through these means. We can prove that the Iranian government or Islamic governments are against human rights, not Islam.
Islam has many interpretations. Look at Saudi Arabia. A woman cannot even drive a car, but many years before in Tunisia, Bangladesh, and Pakistan, a woman could even be president or prime minister. Another example is that cutting off the hands of thieves is in our penal code, but many Islamic countries have banned it, like Tunisia, Egypt, and Malaysia. So which one is slow? Just like in the west, one church accepts gay marriages and one church completely ignores it. Most of them follow Christianity. Which one is right?
Islam is the same. It is our duty as modern Muslims to challenge the Islamic government that we can be Muslims and have more respect for democracy and human rights. In this way we start to challenge Islamic governments.