Why is Bolivar Trask a person of short stature?

It appears the decision to cast Peter Dinklage was made for two main reasons.

First (and arguably foremost), he's very hot property in Hollywood. A quick look at his Wikipedia page can show the amount of awards and nominations he's been up for since Game of Thrones debuted. He also regularly tops fan polls regarding their favorite character. All of this adds up to a convincing reason to cast him in a film (similar to someone like Bryan Cranston, from Breaking Bad, starring in Godzilla).

Secondly, his short stature does appear to be significant - as it has left many observers questioning the decision and making links between his disorder (anchondroplasia) and his character's dislike of mutants.

Peter Dinklage was certainly aware of this. In an interview which also involved Bryan Singer (the director) the following dialogue took place:

To hear "X-Men: Days of Future Past" director Bryan Singer tell it, however, Trask has a lot in common with no less than Adolf Hitler.

Singer: “Trask is, ultimately, a peace lover. He feels that humanity will go on fighting each other unless they find some common element to unite against,” the filmmaker told "Empire" magazine. “Perhaps as Hitler used the Jews as a scapegoat to bond the darker parts of Europe, he’s doing the same thing with mutants. There’s also something interesting about his size. I’m sure he went very underestimated throughout his life. Trask comments on that — I don’t know if it’ll be in the final picture — but he says, ‘I was underestimated, so do not underestimate these creatures.’”

Peter Dinklage, who plays Trask, said he “wouldn’t go so far as [comparing Trask with] Hitler,” but acknowledged similarities between the two.

Dinklage: “I am this guy who’s four and a half feet tall, but my life doesn’t constantly address it,” the "Game of Thrones" star explained. “With me playing that role, I had to think about that stuff. I’m not going to play my violin, but with my dwarfism, I’m a bit of a mutant. I can’t move metal or anything, but I thought of it as self-loathing.”

“Deep down, Trask can be quite sensitive about that aspect of himself,” he continued. “And sorry to go back to Hitler, but he wasn’t a six foot, perfect blond Aryan. He was a short, funny looking fellow. And talk about a mustache!”

So you can see, both actor and director have made no attempt to hide Dinklage's and thus Trask's stature (which is only an issue in the movie, as in the comics he is of an average height). Instead, they've used it to explain some of the prejudices he may feel, given the prejudices he's been exposed to his whole life.

Ultimately, I'd say Dinklage was simply cast as he's such a popular commodity in Hollywood at the moment. But his short stature certainly adds an interesting dimension to the character of Trask and provides extra motivations for his actions.

The fact that Bolivar is of short stature may influence his hatred towards mutants, being a little person could be seen as a mutation, and probably deep down he feels jealous, even angry that these people get awesome powers and he what he gets is to be short

A person with some form of deformity works very well in this role. Even a "Traitor" mutant would've worked very well here by adding more complexity and interesting motivations than just another stock scientist. This character needs a passion and hate towards mutants resulting in his obsession which ultimately culminates in his ahead of his time inventions and the sentinel program.

Or else the viewers would constantly be wondering why is he so obsessed with it all. An ordinary scientist with a "mutant killed my family" type of background story would've worked but a person with some deformity/mutation works infinitely better. He also has a real and very important motivation - fixing his own condition.

Let me elaborate:

1. Self cure - There's no cure for his condition in the human world but with the coming of mutants, where people can change their body shapes/compositions at will, it's beginning to look like a real possibility. A genius (supposedly) level intellect scientist like him would jump at the prospect of studying viable mutations that help cure his own deformity in addition to curing countless diseases. This would also explain why he was so much interested in Mystique.

2. Need for approval - He's been likely oppressed and ignored for most of his life. He's probably given less consideration than other scientists at his job. But now recognizing and fighting mutant problem gave him the opportunity to show that he's actually a very able and highly contributing member of the society. Now he's not only the same as the rest of humans but can even dream of becoming the savior of humanity despite of his short stature.

3. Hate & obsession - Trask perhaps partially identifies his dwarfishness as a form of mutation (which, scientifically speaking, it is). His hate towards mutants allows him to fuel a pseudo-superiority complex - "I'm not as good as normal humans but I'm better than these abominations/mutants and I'm gonna prove it". It's a lot like prisoners turned guards hate the other prisoners or workers turned foremen start hating other workers. It fills a void in his psychological setup (there must be a psychological term for this).

I'd not have been surprised if Trask was revealed to have some minor mutation (more mutant like) himself.

In summary, a pseudo-mutant works better than a normal scientist in this role for his understated but very complex motivations and Peter Dinklage is a great cast. He doesn't look like an evil scientist but his motivations register without any overt back stories.