I don't know, but I suspect that born again might have originally referred to something that isn't even limited to the Christian tradition. (I'm sure there will be those that disagree, perhaps vehemently - be that as it may I am just throwing the idea out there) In the eastern traditions like zen they talk about things like a big death, which may seem to be the opposite but basically it means a death of self, ego or whatever you want to call it, and with that out of the way one can really live. Now from this perspective, if someone is being pushy about their religion, being identified with an emotional experience (having one is not the problem, just if they're stuck on it) and so forth, it can hardly be said they lost the sense of self - it's just new content.
This probably sounds kind of weird to most people, but what I've noticed is that people that don't have much of a sense of self are rather refreshing to be around. When you don't take yourself too seriously there's a natural sense of humor that shines through, and you're less likely to have conflicts with people - not even exchanges such as those where one says: "Well, everyone can believe whatever they want, you have the right to your opinion" in an effort to sound diplomatic or whatever, all the while harboring the feeling that I'm right, they're wrong, and they are not my kind of people because they think differently. Of course, what I'm talking about is not what you think but how you think and behave, it just so happens that when you're less self centered it's easier to take in a broader view. In other words, it's a matter of being free from your 'self.'