Select the wishlist you want to change the visibility for, click on the three-dot icon, and then choose 'Edit.'
When you click on 'Edit,' a window will open where you need to scroll down to the bottom to the 'Visibility' section.
The difference between the three options
Public: Visible to all your friends on your profile, and anyone with the link can view the wishlist.
Hidden: Hidden on your profile, but anyone with the link can view the wishlist.
Private: Only visible to friends you invite to this list and current followers and collaborators of the list. Followers of the list cannot share it with others.
Then press 'Save changes' to complete the action.