Are you sending a transactional email? You can bypass the contact’s marketing preferences for transactional emails by changing the email type to Transactional.
You should not use transactional type emails for all emails to bypass the preferences, this can land you in legal trouble with your local authorities.
Transactional emails are currently not supported by the broadcast feature, they are only supported by funnels or one-off emails sent from the contact actions tab
To change the email type, edit the email, and change the type to transactional.