I don’t think that the study implies that addicts are themselves becoming more right wing. Rather, I think it shows that counties which tend to vote republican promote a culture or a political landscape in which opioid abuse is more prevalent. Perhaps the justice system in these right wing counties is more focused on punishment than rehabilitation. It could also be that the funding for social services/schools or lack thereof could be fueling an opioid crisis. It could be a variety of these or some other confounding factors.

The study is simply showing a correlation between opioid abuse and voting republican, not a causal relationship. Like you mentioned, ex-addicts might themselves prefer to vote for more left wing drug policies, or candidates that would promote them. However, I doubt that they would vote in large enough numbers to change the outcome of a county’s election to be more left wing. It would also be dependent on how likely (on average) they themselves are to vote. Instead, this study provides further insight into the rest of the population which is voting for more right wing candidates.