You have the option of hiding the "Contact Info" section on a workspace from non-owners.
A non-owner is anyone that is not added specifically as an "Owner" on the workspace under the "Members & Access" section. If you are designated as just "Read+Write" or "Read Only" you are NOT an owner.
All you have to do is click on the Admin icon, find "People settings" on the left, and select "Default access." Scroll all the way to the bottom until you find "Default access for Workspace Contacts." Choose the second option "Administrators and workspace owners only" before clicking "Update."
Here is what general user will see when they navigate to a workspace of which they are not an owner:
*NOTE: This affects ALL workspaces in the entire site.