Hey there,

The access mode of every island is always custom by default and this option cannot be changed - this is normal (imagine how your island list would look like if players could set their islands to "public").

Island access rights can be set in more detail below this option, so you can specify who you want to have access to your island:

• if you want the island to be "private", then don't add anyone to the access list
  
• if you wish to make it only accessible to your guild, then add your guild to the access list
  
• and you cannot make it public, for obvious reasons
  

The island permission board uses the same Access Rights interface as everything else (buildings, furniture, hideouts etc.), this is why you see this option - even though it indeed serves no purpose for islands.