Note: This does not in ANY WAY represent my own religious views.
It's possible that C.S. Lewis meant for the Dwarfs to represent the Jews. At the end of The Last Battle, the Dwarfs refused to be 'taken in' by Aslan. It's possible that C.S. Lewis meant for this to represent the Jews refusing to believe in Jesus.
The Jews didn't believe in Jesus. They don't think that he fulfilled the requirements to be the Mashiach (Messiah). I think I read that Christians believe that they'll get hell for that. And, in Narnia, the Dwarfs are refusing to believe in Aslan, leaving themselves to be stuck sitting there, believing that they are in a barn, for eternity.
There's also the fact that the Dwarfs are often presented with beards (quotes eventually), and Jews often wear their beards long.
After posting this, I had been doing some research on what Lewis thought of Judaism. I found Lewis's Trilemma, in which he says:
I am trying here to prevent anyone saying the really foolish thing that people often say about Him: I’m ready to accept Jesus as a great moral teacher, but I don’t accept his claim to be God. That is the one thing we must not say. A man who was merely a man and said the sort of things Jesus said would not be a great moral teacher. He would either be a lunatic — on the level with the man who says he is a poached egg — or else he would be the Devil of Hell.
...As this is almost exactly what Judaism believes, that he was deified by his followers, he seems pretty critical of them.
On this webpage, they make some points:
First, in Luke 23:1-2, the Jews opposed Jesus being their Savior because they were fearful of Him. They feared Him because He did not follow their laws and how could their Messiah not respect their ways.
Similarly, the dwarves were blinded by their fear like they were being held in a dark stable and could not escape. They could not see the paradise that Aslan created and that there were no doors at all on this stable. Secondly, the Jews did not believe in Jesus even though he saved lives and performed miracles in front of them. (John 12:37) In the book, Aslan performed a miracle in front of the dwarves. He made banquet food appear out of nowhere but the dwarves believed that the food was donkey food. Thirdly, to believe in God, one must give up all control. In the Bible, Jesus tells Nicodemus that he must give up all his worldly possessions to have salvation in Him. Nicodemus cannot give up this control. (John 3:1-21) In the book, the main problem for the dwarves is that they do not want Aslan to control them.
So, ways in which the Dwarfs could represent Jews:
Their belief in Aslan's return.
The Dwarfs have always been a little reluctant to believe in Aslan, or at least his return. Remember in Prince Caspian?
"Oh, Aslan!" said Trumpkin cheerily but contemptuously. "What matters much more is that you wouldn't have me."
-Prince Caspian, chapter 6
"But they also say that he came back again," said the Badger sharply.
"Yes, they say," answered Nikabrik, "but you'll notice that we hear precious little about anything he did afterward. He just fades out of the story. How do you explain that, if he really came to life? Isn't it much more likely that he didn't, and that the stories say nothing more about him because there was nothing more to say?"
-Prince Caspian, chapter 12
And the Jews don't believe that Jesus came back to life.
Not believing in miracles performed right in front of them.
Aslan raised his head and shook his mane. Instantly a glorious feast appeared on the Dwarfs' knees: pies and tongues and pigeons and trifles and ices, and each Dwarf had a goblet of good wine in his right hand. But it wasn't much use. They began eating and drinking greedily enough, but it was clear that they couldn't taste it properly. They thought they were eating and drinking only the sort of stuff you might find in a stable.
-The Last Battle, chapter 13
Apparently Jesus did miracles and they still didn't believe that he was the son of God.1 | 2
They are afraid of being 'taken in' and being controlled.
"Well, at any rate there's no Humbug here. We haven't let anyone take us in. The Dwarfs are for the Dwarfs."
"You see," said Aslan. "They will not let us help them. They have chosen cunning instead of belief. Their prison is only in their own minds, yet they are in that prison; and so afraid of being taken in that they cannot be taken out. But come, children. I have other work to do."
-The Last Battle, chapter 13
And apparently from the source I mentioned before, some guy did something like that in the Christian Bible?1 He had to give up his money to do something, and he didn't want to?
In the Bible, Jesus tells Nicodemus that he must give up all his worldly possessions to have salvation in Him. Nicodemus cannot give up this control. (John 3:1-21) In the book, the main problem for the dwarves is that they do not want Aslan to control them.
Also, the Dwarfs have always been old Narnians, even if they've had a rocky history with Aslan. They believe that Narnia is 'not a human country'. This is reminiscent of the Jews believing in one God, but not in Jesus. (Remember the note at the top? Not my views at all.)
Tl;dr: It's fairly likely that C. S. Lewis intended for the Dwarfs to represent Judaism from his point of view.
1My knowledge of Christian theology is very sketchy.
In the Gospel of John, Jesus is said to have performed seven miraculous signs that characterize his ministry, from changing water into wine at the start of his ministry to raising Lazarus from the dead at the end.