Consider some jobs that lean conservative: soldier, police, doctor, religious worker, insurance broker. These seem to be jobs where there are rare big bad things that can go wrong, and you want workers who can help keep them from happening. That explanation can also makes some sense of these other conservative jobs: grader & sorter, electrical contractor, car dealer, trucker, coal miner, construction worker, gas service station worker, non-professor scientist. Conservatives are more focused on fear of bad things, and protecting against them.
Now consider some jobs that lean liberal: professor, journalist, artist, musician, author. Here you might see these jobs as having rare but big upsides. Maybe the focus is on small chances that a worker will cause a rare huge success. This is plausibly the opposite of a conservative focus on rare big losses.
But consider these other liberal jobs: psychiatrist, lawyer, teacher. Here the focus may just be on people who talk well. And that can also make sense of many of the previous list of liberal jobs. It might also makes sense of another big liberal job: civil servant.
I’m not suggesting these are the only factors that influence which jobs are liberal vs. conservative, but they do seem worth exploring.
Added 3Dec: A new article with data.