About the circumstances in Saudi Arabia, Qatar, Turkey, etc. you do not have to say much. But maybe there are Islamically embossed countries that tick something more advanced?
Of course, there are progressive Islamic countries. The conflicts in the Middle East will quickly make the impression that the cause of Islam's problems are. But that's just the case.
The nearby was on a good way in the last century. There were progressive powers in states such as Iran, Iraq, Syria and Egypt who wanted to bring their countries forward. This was also important to liberate oneself from Ottoman backwardness.
The problems with terrorism came later. Likewise, the cause of so-called Failed States (eg Iraq) is a consequence of American foreign policy.
The advanced countries include, for example, the United Arab Emirates, Jordan, Syria Bis on the outbreak of the Civil War.
The great problems are actually only in the states in which the West and at the time of the Cold War also the Soviet Union have too much mixed.
In the past, Turkey was considered the hopefound of the Islamic world. So probably economically as well as what the human rights situation is concerned. That was not always perfect but unfortunately this has worsened massively in recent years.
Mitlerweile I would say that the most advanced Islamic countries are Indonesia and Malaysia. Where economic progress is associated with social backward step.
When looking pure on economic aspects, then the oil mornachia is far ahead, but these are bangHard autocracies.
Do not know what you want out, but in Israel, almost 20% of the population belongs to Islam.
Investations / Things from Israel you know : USB sticks, W-LAN, WhatsApp (formerly ICQ), medical mini cams, Mobile-Eye (camera-based security system for cars such as BMW, Ford, Volvo, etc.), etc.
From the point of view of women, Libya under Gaddafi was the most advanced. He also tried great technical initiatives, for example, water recovery from large ground depth under the desert.
Of course, no one wants to hear that today.