I am hoping this topic will stay focused and not go in 100 different directions.
Maybe I should present my case why I believe Islam has nothing against Secularism, on the contrary supports it and then let others critique it.
I believe the core issue here is justice for all. Those who support secular institutions consider that secularism establish justice & gets away from all different kind of bias. It supports that the citizens of any nation, country or state may not be judged in matters of law by their religion, or any other religion be imposed on them as a state religion.
Well, those who believe in the notion of a so-called Islamic State claim that a TRUE Islamic State would give that justice to its citizens. And I agree with them, because in my opinion a true Islamic state is a secular one in nature.
My proof of the above claim from Quran is as follows.
38: 26/27 * O Dawood ! surely **We have made you a ruler in the land; so judge between men with justice **and do not follow desire, lest it should lead you astray from the path of Allah; (as for) those who go astray from the path of Allah, they shall surely have a severe punishment because they forgot the day of reckoning. *
Allah didn't say with such n' such Torah Law but with Justice. Similarly there are other verses that stress on the need for justice, and steadfastness to justice even if it goes against your very kin.
And a proof of that secular state from Sunnah is AnHazoor (saw) government in Madina.
When he first migrated to Madina, the Jews & the Christians living there took him as their political leader but not a spiritual/religious one. And there is no were in the history that he judged between them according to the Islamic Sharia!
He gave the Jewish people who came to him with problems and dispute the choice of judgment through an Jewish law or an arbitration. When a dispute between a people of two different faiths came, he didn't judge them according to the Islamic law, but according to the common law that they both agreed to before hand or under the confinements of "Mesaq-e-Madina" (covenant of Madina).
So, people say this doesn't constitute a secular state ... because at times he did judge according to the religious laws of the people involved. And therefore, according to the Sunnah we should have a state that has separate laws for each religion!
My response to them is, is it really possible? Not only the that there are hundreds of different religions residing in one country (for example the USA or even some of the African countries where each tribe has his own religion) but even within those religions the sects interpret the law differently. So 73 different laws for Muslims & 73 for Jews and close to that for the Christians, Buddhists and so on is mind boggling.
So, a secular state where with a democratic institution establishes the laws is the only answer! And that's the only way the spirit of Justice so embedded in the Quranic message can be served right!