Overview:
Consent lines opt in or opt out is applying to all lines rather to the specific consent line that opted in or opted out. A Consent line determines to which products or sub-channels consent is given.
Root Cause:
Sub_Channel_Key_vod defines items for consent that are temporary or that may only exist once. This is stamped on the Multichannel_Consent_vod record when consent is captured. Field Level Security (FLS) of the Sub Channel Key field of Multichannel Consent is not granted.

Solution:
Grant FLS to the user profile.
Related Documentation:
CRM Help Documentation: Consent Capture Overview