Kierkegaard was incredibly pedantic and highly accomplished in his field at a very early age. However, he had serious social difficulties. He had a bizarre obsession with his fiancee, Regina Olsen, whom he rejected. He didn't feel he could be married and be a minister at the same time. However, he writes about her quite a bit.
Some of his social difficulties can be attributed to the social climate of Copenhagen and how caustic it seems, they criticized everything and made sport of it. However, people specifically picked on Kierkegaard's difficult-to-read style of writing, repetitiveness (in writing and speech) even referring to him as a parrot.
In Jens Andersen's biography of Andersen, he addresses Andersen's and Kierkegaard's common issues: "loneliness, a fear of women, enthusiasm over fairy tales, an interest in the importance of childhood, and a desire to figure out other people."
Hans Christian Andersen actually inserted him into a play of his as a parrot, that the audience could easily identify, "an exotic bird who philosophically babbles on, constantly shaking his head and sending ripples through his birdlike coiffure and crooked nose.<snip>And many people in the city nodded with recognition at this bird who was so good at 'making a quip, quip, quip' and lavishly scattering philosophical remarks, such as: 'Now, let's be sensible people!'"
Kierkegaard was an ambitious theology student, though obsessed with fairy tales as well, needing to curb his hobby for his studies. However, his first paper was on Andersen, a critique. His disliked Andersen's sentimentality and felt fairy tales should be for adults.
Source: Jens Andersen's, Hans Christian Andersen, A New Life, A Kierkegaard Anthology and some other Kierkegaard source that's not in front of me that I read a long time ago.
I haven't heard anyone discuss Kierkegaard at all since college, let alone if he was an Aspie.
On the surface, Kierkegaard and Andersen have very similar lifestyles. But I think they are dramatically different people.