It helps to clarify the psychological motivations that drive political alignments. Inequality only shifts someone's political alignment when they suffer from it sufficiently, right? Thus the right supports business as usual and forms governments on that basis so long as most voters don't feel that they are victims of inequality. The left does the same so long as most voters feel they'll manage better than the right. Neither left nor right makes any serious attempt to do anything other than make token moves to reduce inequality.
System justification theory helps us understand collective motivations much as paradigm theory does, yet is unhelpful from a common good perspective. It is in our common interest to shift to a sustainable society in which everyone gets provision for a healthy life. Our traditional economy evolved naturally so as to minimise the number of winners and maximise the number of losers, making inequality not only inevitable but exponential. One need only observe the population versus wealth curve for any country to see that.
Therefore inequality is a design problem, and progress will only come from crowd-sourcing the optimal solution. The traditional collusion between the political left and right commits both to the status quo, so the only way to make progress is for those in the political centre to advocate a suitably-designed solution. Academics could facilitate this progress if they shift from analysis to collaboration: selection of the optimal design is the task. Here's an exciting intellectual challenge - form a team to engage the task. Form many such teams! Then hold an international tournament in which all compete. Provoke media coverage to escalate public interest. That will shift everyone out of complacency and defeatism.