We do not provide a method to completely hide or disable the Members Directory functionality. This page is accessible to all users. However, users can only see certain sub-groups, depending on their user account permissions. You may see this support article for details on which each type of user is allowed to see.
Can I keep my information private?
Yes. We do provide a method for users to mark their information private. This is a choice each individual user must make. This cannot be applied on a large scale to multiple users, so each user must make this choice themselves. You may see this support article for instructions on how to set your personal information to "private."