With MC4WP generally I recommend using the Interest groups for this instead of tags. They are easier to manage and options to add them to the form are build into the field editor.
First add the interest group(s) in your Mailchimp account under audience settings, then in your WordPress admin go to MC4WP > Mailchimp, click “renew mailchimp lists” and then go to MC4WP > Form > Fields, and you will see a button to insert the interest group(s) as checkboxes.
Under MC4WP > Form > Settings you can choose if you want to update (add) or overwrite the interest groups when a subscriber already exists.
Hope that helps. If you have any questions, please let me know!