So, do I think that automation causes most people to desire freer markets? No. In the same way that the immigration or globalization doesn't exactly make the working class reach for free markets... it's actually the complete opposite. So they're definitely not reaching right in that sense.
Well, another thing that's often represented on the left vs right is progressivism vs conservatism, and here is where we get to the heart of this pattern. People who want things to change in some uncharted direction, vs people who want things to stay the same or go back to a previous state. Your job is gone due to automation, immigration, or globalization? It's entirely reasonable to reach for the conservative button to make things go back. Populists promising your job back is an appealing message.
Because think about progressivism. Progress is fundamentally just change. Whether the change is good is not a given. While pairings with automation actually do exist that could theoretically usher in better economic outcomes for everyone, i.e. UBI or the like, I don't think most people have faith in our politicians to actually get us there. So the Luddite impulse kicks in, and says "I don't like what's happening, make it stop, take us back to the state where I know I still have a place in our economic system." It's completely understandable. If you want to change things, you have all of the burden to convince people that you're taking them someplace better, and that's no easy feat when they're watching circumstances around them rapidly knocking out their livelihood, and there's someone out there promising they can make it stop and go back to how it was.