That's quite an intelligent objection, and yes - as you would expect, it is also my own perception that these states (I'm thinking of Texas and co.) are more prone to violence and intolerance.
I oftentimes get the feeling that the evangelical churches of the United States teach a Christian lifestyle that is very far from what Christianity means to many individuals in Europe. I would argue that many European churches are far more progressive both in rituals (i.e. equal rights for homosexuals, divorced couples, etc) and in teaching (i.e. a heavier focus on teachings of the New Testament as opposed to the Old Testament).
As such, if we go back to our initial assumption, which is that scriptural basis is cause for contemporary violence, we might construe that much of the "intolerance" found in the areas you mentioned might be due to a focus on the Old Testament laws that condemned homosexuality and promoted views that do not match progressive views.
In my opinion, the difference would once more be that these misconceptions could be cleared up by
encouraging Christians to look into their Bibles
more, not less. The NT details the new covenant, which is -no matter what biblical interpretation you follow- the successor to the covenant of the OT.
In Islam, the more contemporary Hadiths and Suras paint a picture that is more violent than those during the initial stages of Mohammads expansion. There is no real hierarchy that would set the Meccan surahs above the Medinan ones.
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As for religion and crime, at the risk of going too far off-topic, I do believe that this is a very interesting and relevant topic.
I am no expert on the subject.
An interesting article I found was a review that entailed 60 studies on the effects of religion on criminal behavior, which found a protective effect (negative correlation of median r=-0.12). The review itself noted that one of the shortcomings of many studies was the lack of differentiation as according to denomination.
When looking at other parts of contemporary scientific literature on the subject, the effects range from "no deterrent effect" to "deterrent effect", but I have yet to see a study that indicates an increase in violent behavior, apart from the criminological data I provided earlier.
I am somewhat surprised to see that there are no follow-up studies or studies from other areas that actually take the time to plot denomination versus crime data. I would bet that Islam (and perhaps the "OT-Christians" you spoke of) would significantly increase the risk of delinquency.