so the favorite & unfavorited links are actually too seperate buttons - when you click one it triggers a "hide" class then will hide & display the other. basically this hide class toggles between when a character is favorited or not favorited. the hide class is set to dsiplay:none. use inspect element on the favorite links and you will see one of them has the "hide" class assigned to it
when you set the top bar links to display:inline-block you are overriding this hide class, causing them both to show. so set the hide class back to {display:none!important;} in your css & it will resolve the issue