Diamond Tiara and Silver Spoon don’t hate Blank Flanks. Every interaction of them picking on a pony for being a Blank Flank has always been in relation to Apple Bloom, either her, her friends, or her family.
This is because Diamond Tiara and Apple Bloom used to be friends, but at some point, Apple Bloom almost killed Diamond Tiara, albeit by accident, but at the same time, it was due to her poor impulse control. Diamond Tiara because infuriated with Apple Bloom, but because Apple Bloom has a chronic inability to learn from these kinds of experiences, Diamond Tiara gave up on trying to convince Apple Bloom to stop being a reckless idiot, and now cares more about making Apple Bloom’s life miserable, the Blank Flank thing being her most effective means of doing so. Silver Spoon is in on the action because Apple Bloom nearly killed her best friend.