Option 1 -> "Customary" means usual or traditional, which doesn't explain why one should be careful when discussing it.
Option 2 -> "Deniable" means able to be denied, which has no logical connection to needing caution in conversation.
Option 3 -> "Justified" means having valid reasons, which doesn't relate to requiring careful handling.
Option 4 -> "Delicate" means requiring sensitive or careful handling, which perfectly explains why caution is needed.
Hence, Option 4: delicate -> A delicate subject is one that is sensitive or potentially uncomfortable, requiring tactful handling in conversation, which directly explains the need to "take care how you bring it up" -> correct