I was originally going to respond in a comment, but chose to make this a post instead (because, let me tell you, internet, I have a lot of feelings). My shortest opinion on this is: they're right. And they're not. I'll expand on that in a minute, but first a little history.
The story of Beauty and the Beast is old and predates most of the modern, Disneyfied and bowdlerized variations we're familiar with. The basic story - a young woman or girl is married off to a beast, figuratively or literally, and discovers that he is someone she can love - has its own classification in the Aarne-Thompson system, 425-C (a list of stories in that classification can be found here). It has developed and warped throughout time, but there are a few main differences between the usual Beauty and the Beast story and the Disney one. First, often Belle is one of several sisters, who each make requests of their father for gifts, and Belle's request causes him to fall into the Beast's territory. Second, there is no Gaston or enchanted objects; they were late additions likely inspired by a 1940s film of the tale. And lastly - though this is not true of every version, but certainly enough to make it an important feature - the Beast is beast only in name, not in conduct.
Now, back to the Funny Feminist's article. They don't believe that Belle thought she could change the Beast's behavior if she loved him enough. That's fair enough, neither do I. Belle doesn't go into this relationship to change anyone, she just wants to save her father's life.
But is there really no hint of Stockholm Syndrome in the film? Well... no. Regardless of whether or not people want to make it, an argument can pretty much always be made about this movie that it's a story of Stockholm Syndrome. Because the Syndrome is, at its core, a bond a captive forms with a captor basically out of gratitude that the captor isn't actively hurting them. The Beast is her captor, there is no denying that. And it would take an awful lot of justification to convince me that throwing Belle in a dungeon, starving her when she refuses to eat with him, threatening violence if she doesn't obey his wishes and emotionally abusing her with his uncontrolled rages.
So the question isn't really does the Beast treat her badly enough that his one-eighty could bring on Survival Identification Syndrome? The question is would Belle truly be capable of putting her earlier fear aside so fully that she could really love him without it being colored, even in part, by SIS? Maybe she could. Forgiveness can be a powerful thing. But so can the need to not be locked up for the rest of your life with someone who not only acts like a Beast but is a Beast. I can't bring myself to believe that Belle was capable of setting aside that kind of traumatic experience completely. Maybe you can.
Especially when I consider that the relationship with the Beast doesn't occur in a vacuum. Belle also has to deal with Gaston, and although she is capable of rebuffing him with aplomb in the beginning of the movie, by the end he has escalated to threatening to throw her father into a madhouse (essentially a combination prison and freak show, at the time) if she doesn't consent to his proposal. With two abusive* men vying for her attention, it almost creates an artificial narrowing of her choices to just the Beast or Gaston; certainly the movie seems to think so.
I also find it genuinely saddening that the subject of Belle's obligatory "I Want" song, travel and adventure, aren't really addressed. One can certainly consider what she experienced to be an adventure, though frankly it seems more like a nightmare to me. But one of her biggest wishes, to get away from the little scope of her town and travel somewhere new and exciting, gets downgraded to traveling a path she most likely traveled before and getting imprisoned in a castle. Not exactly new, and a little more terrifying than exciting.
Does this mean it's completely unsuitable for kids? Well, no, not necessarily. A lot of people watched it when they were kids without any particular ill effects. But it shouldn't be accepted whole-heartedly, either. It can't be assumed that no one will come away with the message "if you're just nice enough to your abuser, he will become nice in return**" or even "it's not that bad, and besides, I need to stay for the sake of the
So while some people certainly do go overboard in estimating the potential harm in this story - there certainly are positive points, which the Funny Feminist brings up - it's also less than productive to over-idolize it. It's okay to like it. It's okay to hate it. It's okay to acknowledge that it has problems but the animation and music are so kickass that you just don't want to give it up. It's okay. All I ask is that you take a really good look at what it is and decide from there.
* Arguably reformed abuser in the Beast, though it's also important to remember that - to be frank - he's using her as his ticket to humanity. Knowing what we do of him from the beginning, it wouldn't be unreasonable for the more cynical among us to assume that he just wised up and learned how to act nice. You could also argue that his giving her access to the library (which she already had) was the equivalent of candy and flowers after an attack, but I digress.
**Which is arguably the moral of the story and has been for a long time. There's a reason several people with vested interests in fairy tales have theorized that Beauty and the Beast was partly intended to comfort girls in the event that their arranged new husband acted or looked like a beast.