I'd like to know what research has found about whether talking about politics on a scale of left to right biases people in any way. Perhaps to answer questions such as if the scale were to be inverted, would it have any difference?
Yes. In fact, it has been demonstrated in experiments that you can get people to assert they believe the opposite of what they previously said if you can successfully frame the idea with its political polarity inverted.
I can't remember the experiments off the top of my head, but I think this podcast episode touches on it. https://youarenotsosmart.com/2019/03/01/yanss-146-tribal-psychology-rebroadcast/
It has been established that people who hold ideologies, or just very strong political beliefs, are motivated by the perception of whether something is left or right. Objective facts, even reproducibility, are less important.