Your profile on cord can be Visible or Invisible. You can change between the two visibility options with a toggle at the top right of your profile.
Profile visibility is independent from your profile status.
Visible allows hiring managers on cord to see your profile and message you.
Invisible blocks every company from finding your profile - you have to initiate every conversation.
If you changed your work preference in your account to part-time, freelance/contract or internship, your profile status will turn to Not Looking and you will be unable to message companies. If you are looking at permanent positions, definitely go ahead and update your work preference in your profile. The account visibility and open to opportunities toggles will be functional as well as the messaging function.