RE: Getting to know your employees better is not prying into their privacy. 

Interfering with someone's personal information is not a good sign. Whether it is an organization or an individual, it is a very shameful thing. Think for yourself whether you can go to someone and ask them to give you access to your social media. Nowadays, there is so much personal information on social media that even siblings do not know each other's social media access.
Anyway, it does not make any logic to share this information with your organization.