Across 6 studies (involving 2 pre-registrations involving nationally representative samples), 2 longitudinal designs, and over 6,000 participants, these are their core findings:

Moral grandstanders (those scoring high on the moral grandstanding survey) tend to also score high in narcissistic characteristics and also tend to report status-seeking as their fundamental social motive.

There is no relationship between moral grandstanding and political affiliation. However there is a link between moral grandstanding and political polarization: people on the far left and far right are both more likely to score higher in moral grandstanding characteristics than those who are more moderate democrats and republicans.

Moral grandstanders are more likely to report greater moral and political conflict in their daily lives (e.g., “I lost friends because of my political/moral beliefs”) and they report getting into more fights with others on social media because of their political or moral beliefs. This correlation was found even after controlling for other personality traits, and continued over the course of a one-month longitudinal study.