The criticism of Bird is that his films contain characters who are innately superior to the majority. This strikes many as elitist, though common sense tells us that we all know people who have an aptitude for something, whether it's music, math, sports, languages, drawing, etc. It's interesting that the idea of talent has become so controversial.
Many claim that Bird expects his characters to be treated differently than those without their talents, and there's some truth in this, but not in a way that Ayn Rand would endorse. I am no Rand expert, but what I know of her writing is that it is elitist; those who are superior should not be dragged down by the inferior and should it happen, then the superior are justified in withdrawing their talents from society.
As the Slate article points out, the idea of the elite going on strike is nowhere present in Bird's work. Rather than springing from elitism, I think Bird's work springs from artistic frustration and I think his career should make that obvious.
In The Incredibles and in Ratatouille, the characters are trying to exercise their talents in ways that are beneficial. A key scene in The Incredibles is when Bob witnesses a mugging while being dressed down by his boss. His frustration doesn't stem from his inability to exercise his powers, but from the altruistic need to help someone who is being victimized. In Ratatouille, Remy risks his life repeatedly to get closer to cooking, something that would benefit people if only they didn't let their prejudices get in the way. Both are frustrated by a world which stops them from being who they are, even though the world would benefit.
Now look at Bird's career. He was an animation prodigy, being tutored by Disney animators at the age of 14. His time at Disney after Cal Arts did not lead to any films of note. It was a low point in the company's management history, where no one with vision (artistic or economic) was willing to take a chance on the kind of animation that Bird wanted to do. At that time, Disney had Bird, John Lasseter and Tim Burton on staff and essentially wasted them all. Talent went unrecognized and unfulfilled.
Bird tried to get several projects off the ground, such as his animated adaptation of Will Eisner's The Spirit and his own Ray Gunn without success. He didn't get to direct his first animated feature, The Iron Giant, until he was in his forties, twenty years after leaving Cal Arts. In moving into live action, he wanted to make 1906. He took the Mission Impossible film as a way of gaining credibility, but even after the success of that project, he couldn't get 1906 into production. Instead, he directed a film with a link to a Disney theme park. While fans are no doubt happy to hear that Bird will be working on a sequel to The Incredibles, he's going backwards at the age of 57, having to revisit an earlier success. As he's closer to the end of his career than the beginning, there are a limited number of films he has time to make. How many of them will be the films he wants to make as opposed to what Hollywood will allow him to do?
Forget Ayn Rand and look at the animation business. It's filled with artists who would say that they're not doing their best work or are stuck labouring on projects that they have no great love for. It's true across the industry, which is why so many artists are involved in side projects that are an escape from the frustration of their day jobs. Bird has been more successful than most, but he still can't get his chosen projects onto the screen. The Incredibles and Ratatouille are fantasies where characters overcome obstacles to fully realize their talents. Unfortunately for Bird and the rest of us, it rarely happens in life.