Is it very unprofessional to contact people from an old job interview and tell them that I think I've made a mistake?
Dropping out of a search isn't really unprofessional (unless you told them to go to hell I guess - but then it will be way too late to apologize). In that light, and under the assumption that you just dropped out suddenly and politely (as most people do), mailing them is not so much unprofessional as much as it is pointless. As Henning says in a comment: "What are you trying to achieve?"


Get a job with them? Way too late for this - the previous position is either filled or allocated differently. If a new position opens up, you can always apply again.
Apologize? No need for that - people drop out of a job search for all kinds of reasons all the time. They have almost certainly moved on, and so should you.
Just let them know that you now regret your decision? Why would they need to know this, or even care?
Start a collaboration? "Hey, I dropped out of your search a while ago" is hardly the best ice breaker.


We all make mistakes. It's best to learn to let things go.