That email icon only displays if the user is publishing their email to the role viewing the Community Group roster.

For example, if the group contains Candidates and a Non-Teaching Staff member is viewing the roster, they will only see the small email icon if Candidates are displaying their email to Non-Teaching Staff.

To enable email for the given example, you would go to Core:
  1. Select Security > Profile Access
  2. Select Profile Publish Access
  3. Change the drop-down to Candidate
  4. Click Candidate to Non-Teaching Staff
  5. Click Edit
  6. Mark email under Internet Fields
  7. Click Save & Confirm
  8. Click Confirm
Note: Simply replace Candidate and Non-Teaching Staff with the roles you need to turn on access for