I found it kind of funny whenever Renarin popped up. I tend to kind of forget about him, but then he suddenly comes up in the most random situation. Him joining Bridge Four is both completely random and completely understandable, you can see the thought process behind it even if you don't really see how he came to that conclusion.
I did not realize that Renarin was supposed to be autistic, didn't really think it was necessary to explain his actions, actually. He had the poor misfortune of being born to definitely not be a soldier in a military family. His father was considered one of the greatest military leaders and fighters of the time. His brother is a natural leader and best duelist in the country. Considering who Dalinar keeps around him, I imagine that most of the men whom Renarin grew up with were military men. He was effectively brought up believing that weakness was the same thing as uselessness. Combined with a natural social awkwardness, is it any surprise he came out like he did?