Wow. I had no idea about Amy Sedaris. I think this comment from the blog you linked says it all:

By making these jokes that denigrate groups outside her core audience, Sedaris gets to claim the appearance of a transgression without actually taking the risk of challenging her target audience. In other words, she can be celebrated for a daring she doesn’t possess.

So it's like, "Look at how politically incorrect I am! Of course I'm not being serious - I'm a progressive hipster just like you!" and her target audience can laugh knowingly while others won't see or care about the "irony," and will, naturally, take offense at the stereotypes. I found it hard to look at those images.