What if your cousin is doing something frowned upon by society (wearing blackface, spouting racial epithets, etc)? What if it's not frowned upon now, but is at a later date? What if you don't find anything objectionable, but they wouldn't want it shown, and their concerns are borne out later? What if it's completely benign but out of context appears problematic (goofing around with a good friend of a different race and it comes across as something different when only a portion of it is represented)? What if they just have a personal objection to having heir picture posted?

There are many reasons why it's a good idea to at least check that the person is comfortable with it. You shouldn't be liable if they've said it's okay.