There are two ways you can avoid sending campaigns to contacts that requested not receiving emails from you:
Option 1 - Exclusion list
Add the contact to your exclusion list. Doing so ensures they'll never receive a campaign from you.
This exclusion list contains email addresses excluded from all direct and automated campaigns.
Learn how to add contacts to the exclusion list.
Option 2 - Unsubscribe contacts from a list(s)
Manually unsubscribe the contact from all lists in your account. Note that if a contact resubscribes to a list by submitting a form, they will be able to receive campaigns sent to that list.