Moving left as a result of working in gig jobs is a much more common experience than some people in this thread seem to think. Its definately something that has moved me left over the last couple of years.
Yes; in my experience, tons of people who have gig jobs for a long time feel that they're "stuck" in the gig economy and turn to left-wing policy as a potential way out. The only type of work that seems to rival it in terms of making people leftists is retail (another classic "well the employee
chose that abusive work environment" field). Of course there
are also people whose experience with gig jobs leads them to believe that the state, unions, etc. should just butt out of their efforts to provide for themselves, but the idea that that takeaway is somehow default or normative strikes me as ideological fanfiction of the right in the same way that the idea that Uber drivers see themselves as an oppressed underclass is ideological fanfiction of the left.