All you need to do is make sure that all your members personal details are kept secure, so if in written form e.g. membership forms etc.they are kept under lock and key. If in electronic form then again, on a secure computer. In the BSAOC the Membership secretary is the only person who knows the personal details of all members and he has never and never will divulge these to anyone. The Branch Secretaries know the details of those in their local branch but again, they all know they have to keep secure.
Personal details include Name, Address, phone numbers and email addresses.
If a member asks to get in touch with another member, then the request will be passed to said member and its up to him/her to get in touch.
Another thing to be careful of is cc on emails. Better to add them a bcc so the rest can't pick up other email addresses.
It's not Rocket Science, just common sense and your club will be OK. However, you can indemnify yourselves via your club insurance if you want, just in case.