If you do not want Members (such as students) to see other Members, we recommend making them Non-members. That way you have their contact data, but they are not able to view the contact information of other Members.

Go to People, click on the person's name, click the icon Edit this Contact, and toggle Contact is a Member to OFF.

Or, go to People, form a group using Select by Tag, Select All, click the blue Bulk Actions button, and Make Non-member.