I like the idea of your study - it could be valuable for similar future situations.
I think classifying individuals as "liberal" or "conservative" may not be the strongest predictor/descriptor of mask-wearing behavior. Other factors may be coming into play, for example - education level or profession. Where I live there is a high concentration of well-educated, STEM professionals, and conservatives (as in all three of these traits). We saw a very high level of mask-wearing in general and store-policy compliance.
I think dichotomizing a variable such as political ideology is too simplistic to capture its nuances. Based on how you select your sample (i.e. self-identifies as liberal or conservative), you may get those who identify strongly with one side or another. The limited generalizability would hinder the contribution of your work to public policy. I would recommend assessing political ideology on a continuum and capture "moderates." It's possible to be fiscally conservative and socially liberal, so again - what are you really capturing by recruiting using these two terms?
Further, I don't think political ideology is at the core of "reasons to wear/not wear" as mask. I think there are stronger predictor variables.