But the money still goes to charity. Essentially person A is just indirectly donating to their pet charity using political capital. As long as the charity is legit, I don't see the problem.

Right, there is no problem, this is not controversial. The linked article that started this thread is suggesting that somehow Zuckerberg plans to get this tax-advantaged treatment by making gifts to an organization that is not actually charitable. That would be a problem, but I would suggest that the linked article is mistaken in saying that this is what Zuckerberg is doing.