Select the wishlist you want to change the visibility for and click on the icon with the three dots. Choose 'Edit' and go to the section 'Visibility'. There are three options to choose from:
Public: Visible to all your friends on your profile, and anyone with the link can see the wishlist
Hidden: Hidden on your profile, but anyone with the link can see 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 click on 'save changes' to complete the action.