There was a lot less difference in liberties in majority Islamic countries and the majority Christian countries until the 60s' and 70s' when Islamic fundamentalist theocracies got enough popular support to gain power. It is a very complex phenomenon that is largely linked to colonialism and especially de-colonization.

Based purely on books Islam is actually the most advanced of the religious texts. It for example actually grants rights for women that are not found in other Abrahamic religions. Do they actually happen as Quaran and hadiths say? No, they largely don't. But there is a high level of differences between different Islamic countries and that are not explainable by sects they believe in. For hijab (as clothing) Afghanistan and Turkey are very different from burqa to hijab (headscarf) having been banned for decades.

Current people in power in Islamic countries aren't there necessarily because of current popular support. Trying to unravel Gordian's knot of Islam, dictatorship, culture, fundamentalism, colonialism and decolonization is as the name tells pretty impossible., For example, FGM is seen as Islamic practice and while not haram it is not Islamic but cultural one that seems to have at least one center in Kurdisrtan. Only thing prophet Mohammed said about it is that if you have to cut don't cut so severely. Which by Islamic jurisprudence makes only the cutting severely not practice itself haram. One of the Islamic principles is that if it isn't explicitly banned it is allowed. Honor violence is a thing. Part of it is largely cultural and how the majority of Islamic countries are honour based societies.

Of course Islam and especially Muslims have a huge amount of issues with social liberties and human rights. But even worst of it, Islamic terrorism, has been a minority in both casualties and attacks in Western countries. In the US in past 50 years majority of attacks have been linked to alt-right and Christian fundamentalism. The majority of attacks by Islamic terrorist organizations happen in Islamic countries which tells us that either governments or inhabitants are not fundamentalist enough for those groups. The rise of the two biggest of past couple of decades, Al Qaida and ISIS/DAESH can be followed to the actions of Western countries. Former because of armament and training because of Cold War and the latter to the power vacuum left by the Iraq war.

Current issues in Turkey are a lot less Islam related than to things like having autocrat and a culture with ultra nationalistic. For example how Ataturk is seen as something that is closing what is haram. Turkey is following especially civil society and oppositional politicians to close degree. The space for advancement in social liberties and human rights is very narrow and they have no issue deporting, jailing or vanishing people (usually just jailing them in black sites). But that does not differ from Russia for example. Erdogan also has no qualms of for example fucking up the economy even more to gain votes. There are different rules for different types of people. If anyone can skirt the rule of law they will. Tax evasion is more assumed than something notable. But one thing I had no issues with was Islam itself. While as foreigner albeit woman I had more leeway but I did not need it. The biggest culture shocks were not Islam but living under autocrat, my and my organizations actions being followed constantly, wide corruption and the absolutely mind boggling one was getting used to people not caring that things are not functional. Currently, the majority of my Turkish friends who have a way out are leaving. Erdogan's economic decisions for winning elections are already increasing inflation that already was entirely out of hand. You literally had no idea what things would cost tomorrow even before elections. The last earthquake in Turkey destroyed a lot of land that was farmland and with war in Ukraine already causing famine forecast is not great.

The law is the issue, I agree. Not religion as much. People are still given the right to a fair trial. The issue arises when police think they can do random stuff without any reason other than vague and pathetic understandings of the law.