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As a preface, I think the question might benefit from some further clarification. Aside from considering the matter in the light of Scripture, it seems many would likely agree that there is a significant difference between what might be called "responsible gun ownership" and the subculture often highlighted by the media that defiantly and aggressively glorifies gun ownership.
I'm aware of no Scriptural basis on which gun ownership can be advocated. In fact, the first verse that comes to mind is Mt 26:52:
Then Jesus said to him, "Put your sword back into its place. For all who take the sword will perish by the sword."
No historical doctrines come to mind, either. Roman Catholic "Just War" doctrine doesn't seem related to the issue, though someone with better knowledge of the Church of Rome may know otherwise.
The strongest potential connection I can see between the church and the "gun culture" would stem from the independent, uncompromising, perhaps "defiant" character of the Protestant Reformation in relation to the Church of Rome in the 16th century. (Some of Luther's "antics" come to mind). Elements of the same uncompromising approach can be seen in the choice of the Puritans to separate from the Church of England.
But, while I'm not a pacifist, I don't mean to suggest that the Bible encourages gun ownership. As far as I'm aware, it does not.
Upvote:2
Luk 22:36 Then said he unto them, But now, he that hath a purse, let him take it, and likewise his scrip: and he that hath no sword, let him sell his garment, and buy one.
Jesus told the disciples to carry a weapon. The sword in particular the short sword was the most deadly weapon available during the times of Jesus. Many quote this verse in connection with guns because both a weapons which can defend.
Upvote:4
I am unaware of any doctrine that explicitly states such a thing. However, it might be linked to the fact that there is a scriptural basis for defending yourself and your family, although it is a matter of opinion that a gun is the best tool for that.
What I would say is more likely is as Ryan Frame said it in a comment:
[I]t's cultural rather than denominational.
In the USA, where the gun culture you are referring to is most prevalent, patriotism is arguably it's strongest. Often, you will find casual Christians who are ultra-patriotic. These people are generally "red" voters because the "blue" candidates typically support such things as abortion and gay marriage. By default, they become gun supporters because "red" candidates usually are.
When you live in a country where it is not uncommon to display the American flag on the same alter as the Cross of Christ what do you expect?