Cracked starts off by naming mentally ill celebrities as a group society considers it okay to mock. This doesn’t seem surprising. Nowadays people talk a lot about punching-up versus punching-down. But that just means bullies who want to successfully punch down will come up with a way to make it look like they’re punching up. Take a group that’s high-status and wealthy, but find a subset who are actually in serious trouble and mock them, all the while shouting “I’M PUNCHING UP, I’M PUNCHING UP!”. Thus mentally ill celebrities.
The other examples are harder to figure out. I would argue that they’re ones that are easy to victim-blame (ie obesity), ones that punch down on axes orthogonal to the rich-poor axis we usually think about and so don’t look like punching down (ie virginity), or ones that are covertly associated with an outgroup. In every case, I would expect the bullies involved, when they’re called upon, it to loudly protest “But that’s not real bullying! It’s not like [much more classic example of bullying, like mocking the homeless]!” And they will be right. It’s just different enough to be the hot new bullying frontier that most people haven’t caught onto yet.
"Nowadays people talk a lot about punching-up versus punching-down." That is, to put it mildly, a mild way of putting it. Arguing over oppression rankings is one of the most popular online sports ever invented. I mean, there's kind of a funny parallel I've noticed — here I sit each morning, eating breakfast while listening to the cardinals, finches and titmice in the holly bush outside my window shrilly scolding the cat for loitering with intent in the vicinity of their food source. Then, when that gets old, I open the laptop and...observe all the little shrill, scolding birds on Jaybird Street cheering for the morons going tweet, tweet, tweet. At least the feathered birds are pretty to look at.
In keeping with the law of noospheric entropy, the unobjectionable concept that people should refrain from bullying others has decayed into the bumper-sticker slogan of "punching up/down". Like its sibling cliché, privilege-checking, it's become just another tool for reinforcing the social justice pecking order. The multifaceted nature of identity and power means that a simplistic up/down axis will leave out more than it meaningfully encompasses. Our social justice warriors, being the provincial Ameri-centric rubes they are, predictably obsess over the power and privilege held by straight white males, but what happens when two "oppressed" groups are fighting with each other and there's no Whitey to blame it on? In which direction are the punches being thrown when the Nation of Islam is scrapping with the Anti-Defamation League? Are Asian-Americans culturally oppressed by not being "white", or does their educational achievement and superior median income cancel that out?
The metaphor strongly implies that by "punching" in the right direction for long enough, we might achieve sociopolitical parity. In reality, this is just more ends-justify-the-means thinking, and such parity can never exist except as an abstraction. If humans wanted to create a world without oppression, they'd have to stop punching each other, period. But if there's one thing that holds true about people, whatever their race, class, gender, or whathaveyou, it's that they loooooove rationalizing a justification for acting aggressive and mean toward someone who "deserves" it. And on and on it goes.