I don’t hear this as much now as I used to, but here we have another example of an unfortunate translation. The common passage cited is 1 Peter 2:9, and the only version that renders it “peculiar” is the KJV. One place to start when trying to understand a word is to see how it is rendered in other versions. In reviewing them all we can get a often better idea what the original language was intended to convey.
But you are a chosen race, a royal priesthood, a holy nation, a people for his own possession, that you may proclaim the excellencies of him who called you out of darkness into his marvelous light. ((Peter 2:9, ESV))
Other versions more accurately reflect the intended meaning that we are God’s unique possession. This verse is a reference to the holiness of Christians, not our oddness. Remarkably, I have heard a number of Christians use this to claim that people ought to think we are weird. They actually believe that being seen as bizarre or quirky is a mark of true Christianity. People may think we are strange, but that is not our goal.
I have also seen it used as justification to separate ourselves from society and set up a uniquely Christian culture. But does this idea line up with Christ's command to "go into all the world" ((Mark 16:15; Matthew 28:19)) or to be "salt and light" ((Matthew 5:13-16))? Or how about this - does it line up with what the Early Church, the disciples, or Jesus himself actually did? I don't think so.
[Jesus] gave himself for us, that he might redeem us from all iniquity, and purify unto himself a peculiar people, zealous of good works. ((Titus 2:14, KJV))
Setting up isolated communes where we can retreat to Christian music, Christian apparel, and Christian refreshments were not what Peter or Paul had in mind. Seeing weirdness as an ideal to pursue isn't either. While some of our beliefs and practices may be seen as unusual, that's not the goal. We ought to be different in that we pursue good works, correct beliefs, and right practices because we have different priorities than the rest of the world.