ID theft is pretty common, so I really doubt anyone would want their home address published on the internet. But assuming they did agree to you posting that information, you'd need a release from them regarding any consequences from that. Your internet server agreement presumably contains a jurisdictional clause, so you could probably be sued anywhere that agreement provides, regardless of where you happen to be.
It would seem a lot safer to simply hook prospective pen pals up privately and let them do any exchange of information that they opt to do.
See a business lawyer to review your business operations. This may not be the only risky thing you've been doing or thinking about doing.
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This a question that address what you must do and what you probably should do. The should is evident in your concern about having certain standards to protect people's privacy. To the extent you get consent from people for any means of direct communication you should send confirmation of that fact along with instructions on how to retract it after a certain point.
But since you are a website with an online community, why are you talking about physical addresses anyway? Encourage them to communicate online and through your site so you get the traffic and stickiness.