The author of the article has a good point: Romance does seem to be the most frequent basis for censorship. One could argue that it's not the romance in these stories, but the sex; however, as the article points out, books where the heroines are romantically or sexually liberated and pay the price (i.e., die) for their behavior are typically not banned. (I'm not sure if that is actually true -- The Awakening is a challenged book, after all, and she dies in the end... though in a way, it's not really about her committing suicide, but about her taking the only escape available to her.)
Also consider Twilight, which is an extremely controversial subject -- most of the opposition's arguments being about how possessive Edward behaves toward Bella, or how blindly Bella obsesses over him. And Fifty Shades of Grey is challenged because of its heroine's sexual explorations... which happen to be with a similarly troubled hero.
As the NPR article points out, modern romance may not be banned, but it is also considered a shameful thing if you read it -- so much so that many women will hide the fact that they enjoy such "bad" literature.
The author of the NPR article sees all of this as evidence that badly behaved women in fiction aren't allowed to get happy endings -- "badly behaved" meaning that they get to have sex, usually. But I see something a little more sinister: a continuance of the Victorian idea that the purpose of fiction is to moralize, to teach
Don't get me wrong, if I ever have a daughter we are going to have a talk about Twilight (or anything else with unhealthy relationships in it) and why she shouldn't ever let a man treat her that way. But I figure that's the parent's responsibility -- not to prevent your children from being exposed to ideas, but to help them understand and process bad ideas.