Lest us return to the issue of equality.
The idea is unacceptable to Islam.
For the non-believer cannot be the equal of the believer.
Even among the believers only those who subscribe to the three so-called Abrahamic religions: Judaism, Christianity and Islam ( Ahl el-Kitab) are regarded as fully human.
Here is the hierarchy of human worth in Islam:
At the summit are free male Muslims
Next come Muslim male slaves
Then come free Muslim women
Next come Muslim slave women.
Then come free Jewish and /or Christian men
Then come slave Jewish and/or Christian men
Then come slave Jewish and/or Christian women.
Each category has rights that must be respected.
The People of the Book have always been protected and relatively well-treated by Muslim rulers, but often in the context of a form of apartheid known as dhimmitude.
The status of the rest of humanity, those whose faiths are not recognised by Islam or who have no faith at all, has never been spelled out although wherever Muslim rulers faced such communities they often treated them with a certain measure of tolerance and respect ( As in the case of Hindus under the Muslim dynasties of India.)
Non-Muslims can, and have often been, treated with decency, but never as equals.
(There is a hierarchy even for animals and plants. Seven animals and seven plants will assuredly go to heaven while seven others of each will end up in Hell.)
Democracy means the rule of the demos, the common people, or what is now known as popular or national sovereignty.
In Islam, however, power belongs only to God: al-hukm l'illah. The man who exercises that power on earth is known as Khalifat al-Allah, the regent of God.
But even then the Khalifah or Caliph cannot act as legislator. The law has already been spelled out and fixed for ever by God.
The only task that remains is its discovery, interpretation and application.