God alone is not the only message of Qur'an. There are statutes spelt out for Muslims to live by.
True... yet oddly enough, Quran never endorsed Quran alone..

And God alone, as the name implied, doesn't have any correlation with books, any books.
I don't think any Muslim today believe the Qur'an to be less than perfect, all the verses are considered perfect by Muslims.
Dig further, ask further why it's perfect.. and you'll hear weird answers...
It's again.. common... most of the times people are just parroting what they often hear.
Which is the #1 reason why advertising and propaganda works..
Why iPhone is perfect? I dunno, because everyone else said so....
Tell something (whether it's lie or truth doesn't matter) often enough, it will believed to be truthful.
What paved way for the democracy in Indonesia was the authoritarian regime preceding it. If there Muslims that regarded the Qur'an unfit as modern constitution, it is clear that these were only the elites or ruling class.
What paved way for Secularism in Indonesia was diversity.
Also, how democratic is Indonesia now? Wasn't it in Indonesia a Christian governor(Ahok) was tried and imprison for allegedly insulting Qur'an? Isn't it in Aceh, Indonesia, that religious police patrol the street to ensure everyone complies with "Islamic morals"?
More democratic than commonly perceived. Not perfect definitely.. but less bigotry and more democratic compared to other Muslim majority countries, or many other Christian majority or Atheist countries for that matter.
I wouldn't dig on those two examples, as those two unique cases are unique, yet those are just small cases compared to the bigger whole.
Democracy in Indonesia, like other Muslim countries feel like some thing that is thrust on the people, not something that developed organically. It is majoritocracy.
In case you haven't noticed, democracy is a majoritocracy... majority rules.. for good or for worse..
Yet what I believe you should strive against are Bigotry and Fanaticism.