Over ten years ago, one of my God-given spiritual leaders said in a class that King James Onlyism is actively seeking converts and that, unfortunately, seeking peace by refusing to address the issue was not an option. Conflict was coming, and we needed to go on the offensive. This was coming from a man who is well known for standing firm and standing graciously. This was not an invitation to pugnaciousness or sowing discord among brethren.
The school I went to growing up was and is King James Only. And my teachers and principal there have always been gracious toward me, even in their disagreement. (The fact is, we haven’t talked about the issue since I graduated in 1997.) These folks are too godly to be shrill and intemperate about the issue. They don’t make this their one badge of honor as some do. (I once met an unregenerated homeless man whose first question to me was whether or not I use the KJV; and I had an unsaved KJVO bus-kid as a camper at the Wilds who didn’t know the gospel but did know that the NIV should be burned.)
I think one of the best ways to combat KJVOism without being combative is to bring up real-life passages which are difficult or impossible to understand in the KJV. It’s easy to say in general that the KJV just takes a little getting used to; it even has the advantage of being pretty well true (for educated people, anyway). But there are numerous passages that, I’m convinced, will be misunderstood by modern English speakers unless they pick up a modern English translation. My new KJV category will collect instances like these for my and your future reference. The weight of specific examples may overturn the bulkhead stuck in someone’s conscience.
FWIW, the two passages I always think of–two that I think are good to keep in your frontal lobe in case this issue comes up in conversation–are Col. 2:23b and Ps. 37:8.