I was born and raised in Mexico. The semi-official religion in Mexico is Catholicism, as well as in South America, you can see the difference too between South America and, let's say, the US, a country that was founded by protestant Christians. (I wanna spare all the argument about the US foundation,
I know it was never proclaimed an official Christian nation, but it was founded on Christian principles, directly or indirectly) .
The opression against women in South America is far very different from the opression in Islamic countries. Women are not forced to wear veils, and women can work and go to college, they are not stoned by the government,etc. However, and I blame this partly on Catholicism , the gospel was never spread the same as it was in the States. And for what I've seen, when the gospel is not spread accordingly, the hearts of the people of a nation remain unchanged. In Mexico and South America, people don't have the same morals. Drugs, violence, and a clear indifference to real religion (love and truth) are prevalent in those countries. As you say about muslims, there are also Catholics who are not part of this pattern, but the truth is that generally speaking, in Catholic countries, violence and/or poverty are a common thing to see.
I have read the Quran too, I haven't studied it thoroughly to be honest, nor do I have a degree on Quran studies or something, but I've seen that it doesn't have a New Covenant. The Quran is a book full of laws (and history), while the Bible has an OT and a NT. This is important, because the Quran never says ''ok this was the law, now I will provide a way for you to live better" as Jesus did.
In answer to your example, and not wanting to be rude, I think your example doesn't apply just because it is not a real situation. In the real world, you can easily see what Christianity teaches when it comes to basic doctrines. You just need to look around. And why is it ? Because the Bible is available to us, and we can read it, and we can see that killing is wrong, adultery is wrong, poligamy is wrong, etc. I can see your point

and there are cases where we shouldn't believe things are true because it's the popular idea or behavior, but isn't it interesting that noone interprets the Bible as to say things like ''kill the unbelievers'' as an example?
And I know someone will bring the Crusades to discussion, but I wanna remind everybody that in the times of the Crusades, the Bible was not available to people, and the Church(or the Pope) was the only one who could read it .