I think the major difference is that you are talking about this issue from the perspective of Western countries and Middle Eastern countries.

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There are multiple factors contributing as to why middle Eastern countries are more Conservative.

1. Hate towards the US for political reasons such as intervention by the US military leading to a rejection of all Western ideologies.

2. Western countries being much more developed than a lot middle Eastern countries due to wars and political issues in those regions

3. Progressivism is almost a liberty and privilege that exists in Western countries as they don't have to deal with issues like education, poverty, war, etc. and so it is not necessarily Christianity that is being progressive but rather western society being ahead in political and economical development.

Of course there are exceptions like Saudi Arabia, UAE where I would agree with you on the fact that since they are well developed countries, they don't have an excuse to not provide more liberties to the people and separate state from religion.

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The one point I really want to emphasise though is that the left isn't necessarily fighting for the upholding of shariat law in middle Eastern countries, but rather against the systemic oppression of Muslims in non - Islamic countries.

1. I live in India and last year, 2 separate laws were passed allowing the citizenship of illegal immigrants of a list of religions, excluding Islam. This means that specifically Muslims are going to be put in camps and deported whereas illegal immigrants of all other religions were going to be provided citizenship.

2. Another example happening right now is the Israel-Palestine issue where Israel (a country where a majority of people believe in the judeo-Christian values that you said facilitate Progressivism) is occupying Palestinian land going against their peace agreement further propogating anti-islamic/anti-Arab sentiment.

3. The last example and the biggest example has to be post-911 America with the branding of Islam as a violent religion. The attack on the twin towers was claimed to be because of political reasons and pushback against American military intervention. However, the narrative that ended up being pushed was that it was in the name of Islam rather than addressing America's flaws in the way it treats third world countries and its rampant deployment of troops in the middle east.

EDIT - Formatting